BA6993 Statistics Week 1 to 7 Quizzes

 The difference between the lower class limits of adjacent classes provides the

a. class width.

b. number of classes.

c. class limits.

d. class midpoint.

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a Suppose the growth chart at a pediatrician's office is not hung correctly such that it measures children two inches taller than their actual height. If the heights of 10 children are recorded, which of the following is a true statement?

a. The measurements of the heights that were recorded represent a data acquisition error.

b. The children will systematically be two inches shorter.

c. The measurements of the heights that were recorded will be qualitative.

d. The heights will be exactly the same for each child.

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a

The summaries of data, which may be tabular, graphical, or numerical, are referred to as

a. data analytics.

b. descriptive statistics.

c. statistical inference.

d. inferential statistics.

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b

A population is

a. the collection of all items of interest in a particular study.

b. the selection of a random sample.

c. always the same size as the sample.

d. the same as a sample.

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a

In a questionnaire, respondents are asked to mark their gender as male or female. Gender is an example of a(n)

a. categorical variable.

b. quantitative variable.

c. interval-scale variable.

d. ordinal-scale variable.

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a

Income is an example of a variable that uses the

a. ordinal scale.

b. nominal scale.

c. interval scale.

d. ratio scale.

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d

Simulation, which is the use of probability and statistical computer models to better understand risk, falls under the category of

a. prescriptive analytics.

b. predictive analytics.

c. descriptive analytics.

d. diagnostic analytics.

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b

Which of the following variables uses the interval scale of measurement?

a. Time duration

b. Standardized test score

c. Vehicle miles-per-gallon

d. Student ID number

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b

The set of measurements collected for a particular element are called

a. observations.

b. populations.

c. samples.

d. variables.

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a

In a sample of 400 students in a university, 80 or 20% are Business majors. Based on the above information, the school's paper reported that "20% of all the students at the university are Business majors." This report is an example of

a. descriptive statistics.

b. a sample.

c. a population.

d. statistical inference.

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d

Which of the following defines the term "statistics"?

a. Statistics is the art and science of collecting, analyzing, presenting, and interpreting data.

b. Statistics are used only in sports to calculate "stats" for teams and players such as average rushing yards.

c. Statistics refers only to the calculation of numbers, such as a mean.

d. Statistics are rarely useful and informative.

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a

A graphical presentation of the relationship between two quantitative variables is

a. stem-and-leaf display.

b. dot plot.

c. histogram.

d. scatter diagram.

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d

The most common graphical presentation of quantitative data is a

a. pie chart.

b. bar chart.

c. histogram.

d. stem and leaf display.

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c

The total number of data items with a value less than the upper limit for the class is given by the

a. cumulative frequency distribution.

b. cumulative relative frequency distribution.

c. frequency distribution.

d. relative frequency distribution.

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a

A sample of 15 children shows their favorite restaurants:

McDonalds	Luppi's	Mellow Mushroom
Friday's	McDonalds	McDonalds
Pizza Hut	Taco Bell	McDonalds
Mellow Mushroom	Luppi's	Pizza Hut
McDonalds	Friday's	McDonalds

Which of the following is the correct percent frequency for McDonalds?

a. 2%

b. 27%

c. 40%

d. 10%

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c

When the conclusions based upon the unaggregated data can be completely reversed if we look at the aggregated crosstabulation, the occurrence is known as

a. Simpson's paradox.

b. Pareto's rule.

c. Negative correlation.

d. Reverse correlation.

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a

Data that indicate how much or how many are known as

a. cumulative data.

b. relative data.

c. categorical data.

d. quantitative data.

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d

In quality control applications, bar charts are used to identify the most important causes of problems. When the bars are arranged in descending order of height from left to right with the most frequently occurring cause appearing first, the bar chart is called a

a. Simpson,s chart.

b. Cause-and-effect diagram.

c. Stacked bar chart.

d. Pareto diagram.

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d

Which of the following is least useful in making comparisons or showing the relationships of two variables?

a. Stacked bar chart

b. Scatter diagram

c. Stem-and-leaf display

d. Crosstabulation

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c

• Check My Work

A sample of 15 children shows their favorite restaurants:

McDonalds	Luppi's	Mellow Mushroom
Friday's	McDonalds	McDonalds
Pizza Hut	Taco Bell	McDonalds
Mellow Mushroom	Luppi's	Pizza Hut
McDonalds	Friday's	McDonalds

Which of the following is the correct relative frequency for McDonalds?

a. .27

b. .5

c. .6

d. .4

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d

The numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours	Frequency
0 - 9	20
10 - 19	80
20 - 29	200
30 - 39	100

The class width used in this frequency distribution is

a. 39.

b. 10.

c. 9.

d. 4.5.

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b

The measure of dispersion which is not measured in the same units as the original data is the

a. standard deviation.

b. variance.

c. median.

d. coefficient of determination.

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b

During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperatures of the ten-day period

a. can be either negative or positive.

b. must be at least zero.

c. is negative since all the numbers are negative.

d. cannot be computed since all the numbers are negative.

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b

An unusually small or unusually large data value is called

a. a variable.

b. a deviation.

c. an outlier.

d. correlation coefficient.

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c

Which of the following symbols represents the standard deviation of the population?

a. σ2

b. μ

c. x̄

d. σ

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d

The median of a sample will always equal the

a. 50th percentile.

b. (smallest value + largest value)/2.

c. (Q1 + Q3)/2.

d. Q4/2.

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a

Given the following information:

Standard deviation = 8
Coefficient of variation = 64%
The mean would then be

a. 1.25.

b. 8.

c. 12.5.

d. 0.64.

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c

The closing stock price of MNM Corporation for the last 7 trading days is shown below.

Day	Stock Price
1	84
2	87
3	84
4	88
5	85
6	90
7	91

The variance is

a. 8.

b. 81.

c. 9.

d. 2.828.

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a

When n-1 is used in the denominator to compute variance,

a. the data set is a population.

b. the data set could be either a sample or a population.

c. the data set is a sample.

d. the data set is from a census.

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c

Which of the following is a possible reason for an outlier in a data set?

a. A mistake was made while taking a measurement or entering it into the computer.

b. The individual in question belongs to a different group than the bulk of individuals measured.

c. The outlier is a legitimate data value and represents natural variability for the group and variables measured.

d. All of these choices are possible reasons for an outlier.

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d

A researcher has collected the following sample data.

5	12	6	8	5
6	7	5	12	4

The 75th percentile is

a. 7.5.

b. 7.

c. 9.

d. 8.

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c

The sample size

a. is always smaller than the population size.

b. can be larger or smaller than the population size.

c. is always equal to the size of the population.

d. can be larger than the population size.

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a

Local residents were surveyed for their satisfaction with the local government. The responses were recorded as follows: 0-not satisfied, 1-somewhat dissatisfied, 2-satisfied, 3-very satisfied. The variable recorded is an example of what type of variable?

a. Variable measured on the ordinal scale

b. Quantitative variable

c. Variable measured on the interval scale

d. Variable measured on the ratio scale

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d

Different methods of developing useful information from large data bases are dealt with under

a. big data.

b. data warehousing.

c. data mining.

d. data manipulation.

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c

The data measured on ordinal scale exhibits all the properties of data measured on

a. nominal and interval scales.

b. ratio scale.

c. nominal scale.

d. interval scale.

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c

A characteristic of interest for the elements is called a

a. sample.

b. variable.

c. data set.

d. quality.

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b

The height of a building, measured in feet, is an example of

a. feet data.

b. quantitative data.

c. either categorical or quantitative data.

d. categorical data.

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b

In experimental studies, the variable of interest

a. must be numerical.

b. is not controlled.

c. cannot be numerical.

d. is controlled.

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d

In a questionnaire, respondents are asked to mark their gender as male or female. The scale of measurement for gender is

a. ratio scale.

b. nominal scale.

c. ordinal scale.

d. interval scale.

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b

Data collected over several time periods are

a. time controlled data.

b. cross-sectional data.

c. categorical data.

d. time series data.

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d

Data collected at the same, or approximately the same point in time are

a. time series data.

b. approximate time series data.

c. cross-sectional data.

d. approximate data.

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c

If a negative relationship exists between two variables, x and y, which of the following statements is true?

a. As x decreases, y decreases.

b. As x increases, y increases.

c. As x decreases, y stays the same.

d. As x increases, y decreases.

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d

In a cumulative percent frequency distribution, the last class will have a cumulative percent frequency equal to

a. the total number of elements in the data set.

b. one.

c. 100.

d. None of these alternatives are correct.

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c

The percent frequency of a class is computed by

a. dividing the relative frequency by 100.

b. adding 100 to the relative frequency.

c. multiplying the relative frequency by 100.

d. multiplying the relative frequency by 10.

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c

Which of the following is a graphical summary of a set of data in which each data value is represented by a dot above the axis?

a. Crosstabulation

b. Histogram

c. Box plot

d. Dot plot

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d

Data that provide labels or names for categories of like items are known as

a. label data.

b. category data.

c. categorical data.

d. quantitative data.

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c

In quality control applications, bar charts are used to identify the most important causes of problems. When the bars are arranged in descending order of height from left to right with the most frequently occurring cause appearing first, the bar chart is called a

a. Simpson,s chart.

b. Pareto diagram.

c. Stacked bar chart.

d. Cause-and-effect diagram.

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b

A frequency distribution is a tabular summary of data showing the

a. percentage of items in several classes.

b. relative percentage of items in several classes.

c. number of items in several classes.

d. fraction of items in several classes.

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c

Consider the following graphical summary.

This is an example of a _____.

a. percent frequency distribution

b. relative frequency distribution

c. bar chart

d. pie chart

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d

A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.

Undergraduate Major
Graduate School	Business	Engineering	Others	Total
Yes	70	84	126	280
No	182	208	130	520
Total	252	292	256	800

Of those students who are planning on going to graduate school, what percentage are majoring in engineering?

a. 10.5

b. 30.0

c. 40.4

d. 28.8

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b

For stem-and-leaf displays where the leaf unit is not stated, the leaf unit is assumed to equal

a. 1.

b. 10.

c. 0.

d. -1.

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a

The variance of the sample

a. cannot be zero.

b. can never be negative.

c. can be negative.

d. cannot be less than one.

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b

Statements about the proportion of data values that must be within a specified number of standard deviations of the mean can be made using

a. Chebyshev's theorem.

b. A five-number summary.

c. Percentiles.

d. The empirical rule.

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a

Which of the following symbols represents the variance of the population?

a. μ

b. σ2

c. x̄

d. σ

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b

The geometric mean of 2, 4, 8 is

a. 4.67.

b. 16.

c. 5.0.

d. 4.0.

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d

Suppose a sample of 45 measurements gave a data set with a range of –8 to –22. The standard deviation of the measurements

a. is negative since all the numbers are negative.

b. cannot be computed since all the numbers are negative.

c. can be either negative or positive.

d. must be at least zero.

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d

Using the following data set of monthly rainfall amounts recorded for 10 randomly selected months in a two-year period, what is the five-number summary?

                     Sample data (in inches): 2, 8, 5, 0, 1, 5, 7, 5, 2, .5

a. 2, 5, 5, 5, .5

b. .5, 2, 5, 7, 8

c. 0, 1, 5, 5, 8

d. 0, 1, 3.5, 5, 8

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d

The difference between the largest and the smallest data values is the

a. range.

b. interquartile range.

c. variance.

d. coefficient of variation.

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a

In computing the mean of a sample, the value of ∑xi is divided by

a. n + 1.

b. n - 2.

c. n.

d. n - 1.

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c

The 75th percentile is referred to as the

a. third quartile.

b. second quartile.

c. first quartile.

d. fourth quartile.

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a

The measure of variability easiest to compute, but seldom used as the only measure, is the

a. range.

b. standard deviation.

c. variance.

d. interquartile range.

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a

Temperature is an example of a variable that uses

a. the ordinal scale.

b. the interval scale.

c. either the ratio or the ordinal scale.

d. the ratio scale.

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b

Arithmetic operations are inappropriate for

a. both categorical and quantitative data.

b. large data sets.

c. quantitative data.

d. categorical data.

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d

Dr. Kurt Thearling, a leading practitioner in the field, defines data mining as "the _________ extraction of _________ information from databases".

a. timely, accurate

b. automated, predictive

c. intentional, useful

d. thorough, insightful

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b

In a sample of 1,600 registered voters, 912 or 57% approve of the way the President is doing his job. A political pollster estimates: "Fifty-seven percent of all voters approve of the President." This statement is an example of

a. a sample.

b. statistical inference.

c. descriptive statistics.

d. a population.

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b

Income is an example of

a. nominal data.

b. categorical data.

c. quantitative data.

d. either categorical or quantitative data.

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c

On a street, the houses are numbered from 300 to 450. The house numbers are examples of

a. quantitative data.

b. categorical data.

c. both quantitative and categorical data.

d. neither quantitative nor categorical data.

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b

The summaries of data, which may be tabular, graphical, or numerical, are referred to as

a. statistical inference.

b. data analytics.

c. descriptive statistics.

d. inferential statistics.

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c

Local residents were surveyed for their satisfaction with the local government. The responses were recorded as follows: 0-not satisfied, 1-somewhat dissatisfied, 2-satisfied, 3-very satisfied. The variable recorded is an example of what type of variable?

a. Variable measured on the ratio scale

b. Variable measured on the interval scale

c. Quantitative variable

d. Variable measured on the ordinal scale

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a

For ease of data entry into a university database, 1 denotes that the student is an undergraduate and 2 indicates that the student is a graduate student. In this case data are

a. categorical.

b. either categorical or quantitative.

c. neither categorical nor quantitative.

d. quantitative.

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a

Ordinary arithmetic operations are meaningful

a. only with quantitative data.

b. only with categorical data.

c. with neither quantitative or categorical data.

d. either with quantitative or categorical data.

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a

A sample of 15 children shows their favorite restaurants:

McDonalds	Luppi's	Mellow Mushroom
Friday's	McDonalds	McDonalds
Pizza Hut	Taco Bell	McDonalds
Mellow Mushroom	Luppi's	Pizza Hut
McDonalds	Friday's	McDonalds

Which of the following is the correct frequency distribution?

a. McDonalds 4, Friday's 3, Pizza Hut 1, Mellow Mushroom 4, Luppi's 3, Taco Bell 1

b. McDonalds 6, Friday's 2, Pizza Hut 2, Mellow Mushroom 2, Luppi's 2, Taco Bell 1

c. McDonalds 6, Friday's 1, Pizza Hut 3, Mellow Mushroom 1, Luppi's 2, Taco Bell 2

d. None of these alternatives are correct.

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b

In a cumulative percent frequency distribution, the last class will have a cumulative percent frequency equal to

a. the total number of elements in the data set.

b. 100.

c. one.

d. None of these alternatives are correct.

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b

A graphical method that can be used to show both the rank order and shape of a distribution of data simultaneously is a

a. stem-and-leaf display.

b. dot plot.

c. relative frequency distribution.

d. pie chart.

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a

he numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours	Frequency
0 -9	20
10 - 19	80
20 - 29	200
30 - 39	100

The relative frequency of students working 10 - 19 hours per week is

a. .25

b. .80

c. .40

d. .20

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d

The difference between the lower class limits of adjacent classes provides the

a. class width.

b. number of classes.

c. class limits.

d. class midpoint.

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a

The sum of frequencies for all classes will always equal

a. 1.

b. the number of classes.

c. the number of elements in a data set.

d. a value between 0 and 1.

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c

Information on the number of new teachers hired in a school district for each of four years is given in the table below.

The percent frequency of new hires in 2019 is _____.

a. 80%

b. 40%

c. 10%

d. 25%

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b

What types of variables can be displayed by a scatter diagram?

a. Two quantitative variables

b. Two qualitative variables

c. One quantitative and one qualitative variable

d. Only two discrete quantitative variables

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a

The numerical value of the variance

a. is always smaller than the numerical value of the standard deviation.

b. is negative if the mean is negative.

c. is always larger than the numerical value of the standard deviation.

d. can be larger or smaller than the numerical value of the standard deviation.

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d

The __________ can be interpreted as the number of standard deviations a data value is from the mean of all the data values.

a. correlation coefficient

b. skewness

c. z-score

d. coefficient of variation

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c

The most frequently occurring value of a data set is called the

a. median.

b. range.

c. mode.

d. mean.

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c

If a data set has an even number of observations, the median

a. cannot be determined.

b. is the average value of the two middle items when all items are arranged in ascending order.

c. must be equal to the mean.

d. is the average value of the two middle items.

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b

The heights (in inches) of 25 individuals were recorded and the following statistics were calculated

mean = 70	range = 20
mode = 73	variance = 784
median = 74

The coefficient of variation equals

a. 1120%.

b. 0.4%.

c. 11.2%.

d. 40%.

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d

From a population of size 1,000, a random sample of 100 items is selected. The mean of the sample

a. must be 10 times larger than the mean of the population.

b. must be 10 times smaller than the mean of the population.

c. can be larger, smaller or equal to the mean of the population.

d. must be equal to the mean of the population, if the sample is truly random.

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c

The sample variance

a. is always larger than the true value of the population variance.

b. could be smaller, equal to, or larger than the true value of the population variance.

c. can never be zero.

d. is always smaller than the true value of the population variance.

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b

Which of the following symbols represents the mean of the sample?

a. μ

b. σ2

c. σ

d. x̄

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d

Which of the following provides a measure of central location for the data?

a. Range

b. Variance

c. Standard deviation

d. Mean

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d

Suppose a sample of 45 measurements gave a data set with a range of –8 to –22. The standard deviation of the measurements

a. must be at least zero.

b. is negative since all the numbers are negative.

c. can be either negative or positive.

d. cannot be computed since all the numbers are negative.

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a

Statistical studies in which researchers control variables of interest are

a. observational studies.

b. experimental studies.

c. control observational studies.

d. non-experimental studies.

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b

Income is an example of

a. categorical data.

b. nominal data.

c. either categorical or quantitative data.

d. quantitative data.

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d

The most common type of observational study is

a. a survey.

b. an experiment.

c. a debate.

d. a statistical inference.

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a

Suppose the growth chart at a pediatrician's office is not hung correctly such that it measures children two inches taller than their actual height. If the heights of 10 children are recorded, which of the following is a true statement?

a. The children will systematically be two inches shorter.

b. The measurements of the heights that were recorded represent a data acquisition error.

c. The measurements of the heights that were recorded will be qualitative.

d. The heights will be exactly the same for each child.

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b

The subject of data mining deals with

a. computing the average for data.

b. methods for developing useful decision-making information from large data bases.

c. computational procedure for data analysis.

d. keeping data secure so that unauthorized individuals cannot access the data.

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b

Arithmetic operations are inappropriate for

a. both categorical and quantitative data.

b. quantitative data.

c. large data sets.

d. categorical data.

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d

The weight of a candy bar in ounces is an example of

a. categorical data.

b. quantitative data.

c. weight data.

d. either categorical or quantitative data.

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b

Which of the following variables is quantitative?

a. Phone number

b. Zip code

c. Weight of a package

d. All of these variables are quantitative.

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c

An interviewer has made an error in recording the data. This type of error is known as

a. a non-experimental error.

b. a data acquisition error.

c. an experimental error.

d. a conglomerate error.

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b

Local residents were surveyed for their satisfaction with the local government. The responses were recorded as follows: 0-not satisfied, 1-somewhat dissatisfied, 2-satisfied, 3-very satisfied. The variable recorded is an example of what type of variable?

a. Quantitative variable

b. Variable measured on the ratio scale

c. Variable measured on the interval scale

d. Variable measured on the ordinal scale

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b

The proper way to construct a stem-and-leaf display for the data set {62, 67, 68, 73, 73, 79, 91, 94, 95, 97} is to

a. include a stem labeled '(8)' and enter no leaves on the stem.

b. include a stem labeled '8' and enter no leaves on the stem.

c. include a stem labeled '8' and enter one leaf value of '0' on the stem.

d. exclude a stem labeled '8.

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b

Which of the following cannot be conveyed using a stem-and-leaf display? (Assume that the entire values are used in creating the stem-and-leaf display.)

a. The order in which the observations were taken

b. The original data values

c. The shape of a data set

d. The rank order of the observations

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a

Which of the following is least useful in making comparisons or showing the relationships of two variables?

a. Scatter diagram

b. Stem-and-leaf display

c. Crosstabulation

d. Stacked bar chart

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b

A researcher is gathering data from four geographical areas designated: South = 1; North = 2; East = 3; West = 4. The designated geographical regions represent

a. categorical data.

b. quantitative data.

c. either categorical or quantitative data.

d. crosstabular data.

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a

The percent frequency of a class is computed by

a. multiplying the relative frequency by 100.

b. multiplying the relative frequency by 10.

c. adding 100 to the relative frequency.

d. dividing the relative frequency by 100.

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a

The relative frequency of a class is computed by

a. dividing n by cumulative frequency of the class.

b. dividing the frequency of the class by the number of classes.

c. dividing the frequency of the class by n.

d. dividing the cumulative frequency of the class by n.

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c

A frequency distribution is a tabular summary of data showing the

a. percentage of items in several classes.

b. relative percentage of items in several classes.

c. number of items in several classes.

d. fraction of items in several classes.

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c

A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.

Undergraduate Major
Graduate School	Business	Engineering	Others	Total
Yes	70	84	126	280
No	182	208	130	520
Total	252	292	256	800

The above crosstabulation shows

a. column percentages.

b. row percentages.

c. frequencies.

d. overall percentages.

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Solution

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c

Which of the following types of data cannot be appropriately displayed by a histogram?

a. Cumulative frequency

b. Relative frequency

c. Frequency

d. Percent frequency

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Solution

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a

Which of the following is a measure of variability?

a. Quartiles

b. Interquartile range

c. Geometric mean

d. Percentiles

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b

From a population of size 400, a random sample of 40 items is selected. The median of the sample

a. must be 10, since 400 divided by 40 is 10.

b. must be 200, since 400 divided by 2 is 200.

c. must be equal to the median of population, if the sample is truly random.

d. None of these alternatives are correct.

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d

 numerical value used as a summary measure for a sample, such as sample mean, is known as a

a. population mean.

b. sample statistic.

c. population parameter.

d. sample parameter.

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b

The median of a sample will always equal the

a. (smallest value + largest value)/2.

b. (Q1 + Q3)/2.

c. Q4/2.

d. 50th percentile.

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Solution

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d

An important numerical measure of the shape of a distribution is the

a. z-score.

b. variance.

c. skewness.

d. coefficient of variation.

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c

The sample variance

a. is always larger than the true value of the population variance.

b. can never be zero.

c. could be smaller, equal to, or larger than the true value of the population variance.

d. is always smaller than the true value of the population variance.

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c

The variance can never be

a. negative.

b. smaller than the standard deviation.

c. zero.

d. larger than the standard deviation.

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a

The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated.

mean = 160	range = 60
mode = 165	variance = 324
median = 170

The coefficient of variation equals

a. 203.12%.

b. 0.1125%.

c. 0.20312%.

d. 11.25%.

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Solution

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d

The measure of location which is the most likely to be influenced by extreme values in the data set is the

a. mean.

b. mode.

c. median.

d. range.

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Solution

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a

Which of the following is not a measure of variability?

a. The 50th percentile

b. The interquartile range

c. The range

d. The standard deviation

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Solution

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a

Quantitative data

a. are always non-numeric.

b. are always numeric.

c. are never numeric.

d. may be either numeric or non-numeric.

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b

A characteristic of interest for the elements is called a

a. data set.

b. sample.

c. variable.

d. quality.

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c

The height of a building, measured in feet, is an example of

a. feet data.

b. either categorical or quantitative data.

c. categorical data.

d. quantitative data.

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d

The entities on which data are collected are

a. elements.

b. populations.

c. samples.

d. observations.

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Solution

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a

Which of the following variables is quantitative?

a. Phone number

b. Zip code

c. Weight of a package

d. All of these variables are quantitative.

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c

Local residents were surveyed for their satisfaction with the local government. The responses were recorded as follows: 0-not satisfied, 1-somewhat dissatisfied, 2-satisfied, 3-very satisfied. The variable recorded is an example of what type of variable?

a. Quantitative variable

b. Variable measured on the ratio scale

c. Variable measured on the interval scale

d. Variable measured on the ordinal scale

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b

Statistical inference

a. refers to the process of drawing inferences about the sample based on the characteristics of the population.

b. is the same as descriptive statistics.

c. is the process of drawing inferences about the population based on the information taken from the sample.

d. is the same as a census.

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c

In a sample of 1,600 registered voters, 912 or 57% approve of the way the President is doing his job. The 57% approval is an example of

a. descriptive statistics.

b. a sample.

c. statistical inference.

d. a population.

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a

The number of observations will always be the same as the

a. population size.

b. number of variables.

c. sample size.

d. number of elements.

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d

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The summaries of data, which may be tabular, graphical, or numerical, are referred to as

a. statistical inference.

b. descriptive statistics.

c. data analytics.

d. inferential statistics.

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b

In a sample of 400 students in a university, 80 or 20% are Business majors. Based on the above information, the school's paper reported that "20% of all the students at the university are Business majors." This report is an example of

a. descriptive statistics.

b. a population.

c. a sample.

d. statistical inference.

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d

Many data analysts define big data by referring to the three V's of data, which include all of the following except

a. Volume.

b. Velocity.

c. Validity.

d. Variety.

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c

Some hotels ask their guests to rate the hotel's services as excellent, very good, good, and poor. This is an example of the

a. ordinal scale.

b. nominal scale.

c. ratio scale.

d. interval scale.

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a

Data collected at the same, or approximately the same, point in time would be _____ data.

a. cross-sectional

b. nominal

c. time series

d. qualitative

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a

The number observations in a complete data set having 10 elements and 5 variables is

a. 5.

b. 25.

c. 50.

d. 10.

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d

The sample size

a. is always smaller than the population size.

b. is always equal to the size of the population.

c. can be larger than the population size.

d. can be larger or smaller than the population size.

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a

Which of the following defines the term "statistics"?

a. Statistics are rarely useful and informative.

b. Statistics is the art and science of collecting, analyzing, presenting, and interpreting data.

c. Statistics refers only to the calculation of numbers, such as a mean.

d. Statistics are used only in sports to calculate "stats" for teams and players such as average rushing yards.

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b

A characteristic of interest for the elements is called a

a. sample.

b. data set.

c. variable.

d. quality.

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c

Which of the following is not an example of a firm that sells or leases business database services to clients?

a. Bloomberg

b. Census Bureau

c. Dow Jones & Co.

d. Dun & Bradstreet

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b

Local residents were surveyed for their satisfaction with the local government. The responses were recorded as follows: 0-not satisfied, 1-somewhat dissatisfied, 2-satisfied, 3-very satisfied. The variable recorded is an example of what type of variable?

a. Variable measured on the ordinal scale

b. Variable measured on the ratio scale

c. Quantitative variable

d. Variable measured on the interval scale

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b

The relative frequency of a class is computed by

a. dividing the frequency of the class by the number of classes.

b. dividing n by cumulative frequency of the class.

c. dividing the cumulative frequency of the class by n.

d. dividing the frequency of the class by n.

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d

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Which of the following graphical methods shows the relationship between two variables?

a. Dot plot

b. Crosstabulation

c. Histogram

d. Pie chart

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b

A researcher is gathering data from four geographical areas designated: South = 1; North = 2; East = 3; West = 4. The designated geographical regions represent

a. crosstabular data.

b. categorical data.

c. quantitative data.

d. either categorical or quantitative data.

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Solution

Correct Response

b

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.85

b. 0.85

c. 0.25

d. 0.71

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d

The most common graphical presentation of quantitative data is a

a. pie chart.

b. stem and leaf display.

c. bar chart.

d. histogram.

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d

The difference between the lower class limits of adjacent classes provides the

a. class limits.

b. class midpoint.

c. number of classes.

d. class width.

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d

A graphical method that can be used to show both the rank order and shape of a distribution of data simultaneously is a

a. dot plot.

b. stem-and-leaf display.

c. relative frequency distribution.

d. pie chart.

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b

A survey of 400 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.

What percentage of the undergraduates surveyed are majoring in Engineering?

a. 400%

b. 42%

c. 151%

d. 38%

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d

Information on the number of new teachers hired in a school district for each of four years is given in the table below.

The percent frequency of new hires in 2019 is _____.

a. 10%

b. 80%

c. 40%

d. 25%

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c

The sum of the relative frequencies for all classes will always equal

a. the sample size.

b. one.

c. the number of classes.

d. any value larger than one.

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b

A display used to compare the frequency, relative frequency or percent frequency of two categorical variables is a

a. stacked bar chart.

b. pie chart.

c. scatter diagram.

d. stem-and-leaf display.

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a

In a cumulative frequency distribution, the last class will always have a cumulative frequency equal to

a. 100%.

b. 10.

c. one.

d. the total number of elements in the data set.

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d

The sum of frequencies for all classes will always equal

a. a value between 0 and 1.

b. 1.

c. the number of elements in a data set.

d. the number of classes.

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c

A frequency distribution is a tabular summary of data showing the

a. number of items in several classes.

b. relative percentage of items in several classes.

c. percentage of items in several classes.

d. fraction of items in several classes.

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a

The numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours	Frequency
0 -9	20
10 - 19	80
20 - 29	200
30 - 39	100

The cumulative percent frequency for students working less than 20 hours per week is

a. 100%.

b. 80%.

c. 20%.

d. 25%.

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d

When the conclusions based upon the unaggregated data can be completely reversed if we look at the aggregated crosstabulation, the occurrence is known as

a. Pareto's rule.

b. Simpson's paradox.

c. Reverse correlation.

d. Negative correlation.

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b

The most common graphical presentation of quantitative data is a

a. histogram.

b. stem and leaf display.

c. bar chart.

d. pie chart.

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Solution

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a

The numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours	Frequency
0 -9	20
10 - 19	80
20 - 29	200
30 - 39	100

The relative frequency of students working 10 - 19 hours per week is

a. .40

b. .25

c. .20

d. .80

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c

The relative frequency of a class is

a. equal to the frequency of the class multiplied by 100%.

b. equal to the frequency of the class divided by the total number of observations, n.

c. equal to the frequency of the class.

d. always equal to 1%.

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b

The percentage of data values that must be within one, two, and three standard deviations of the mean for data having a bell-shaped distribution can be determined using

a. Chebyshev's theorem.

b. Percentiles.

c. A five-number summary.

d. The empirical rule.

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d

During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperatures of the ten-day period

a. can be either negative or positive.

b. cannot be computed since all the numbers are negative.

c. must be at least zero.

d. is negative since all the numbers are negative.

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c

The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated.

mean = 160	range = 60
mode = 165	variance = 324
median = 170

The coefficient of variation equals

a. 0.20312%.

b. 0.1125%.

c. 11.25%.

d. 203.12%.

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Solution

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c

The measure of dispersion which is not measured in the same units as the original data is the

a. median.

b. coefficient of determination.

c. variance.

d. standard deviation.

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c

Which of the following is not a measure of variability of a single variable?

a. Standard deviation

b. Covariance

c. Range

d. Interquartile range

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b

The sample variance

a. could be smaller, equal to, or larger than the true value of the population variance.

b. is always smaller than the true value of the population variance.

c. can never be zero.

d. is always larger than the true value of the population variance.

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a

The geometric mean of five observations is the

a. fifth root of the product of the 5 observations.

b. same as their mean.

c. square root of the product of the 5 observations.

d. same as their weighted mean.

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a

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The geometric mean of 1, 1, 8 is

a. 2.0.

b. 3.0.

c. 3.33.

d. 10.0.

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a

When the data are skewed to the right, the measure of Skewness will be

a. positive.

b. one.

c. negative.

d. zero.

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a

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Generally, which one of the following is the least appropriate measure of central tendency for a data set that contains outliers?

a. Median

b. Mean

c. 50th percentile

d. 2nd quartile

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Solution

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b

An important numerical measure of the shape of a distribution is the

a. z-score.

b. coefficient of variation.

c. skewness.

d. variance.

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Solution

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c

The geometric mean of 1, 1, 8 is

a. 2.0.

b. 3.33.

c. 10.0.

d. 3.0.

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a

Which of the following symbols represents the mean of the population?

a. σ

b. μ

c. σ2

d. x̄

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b

If the coefficient of variation is 40% and the mean is 70, then the variance is

a. 1.75.

b. 2800.

c. 28.

d. 784.

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d

In a five number summary, which of the following is not used for data summarization?

a. The largest value

b. The 25th percentile

c. The smallest value

d. The mean

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d

In computing descriptive statistics for grouped data, the data values in each class are approximated using the

a. class range.

b. class midpoint.

c. class upper limits.

d. class lower limits.

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b

The mean of a sample

a. is computed by summing all the data values and dividing the sum by the number of items.

b. is computed by summing the data values and dividing the sum by (n - 1).

c. is always smaller than the mean of the population.

d. is always equal to the mean of the population.

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a

The variance of a sample of 169 observations equals 576. The standard deviation of the sample equals

a. 28,561.

b. 24.

c. 13.

d. 576.

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b

The numerical value of the variance

a. is always larger than the numerical value of the standard deviation.

b. can be larger or smaller than the numerical value of the standard deviation.

c. is negative if the mean is negative.

d. is always smaller than the numerical value of the standard deviation.

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b

The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated.

mean = 160	range = 60
mode = 165	variance = 324
median = 170

The coefficient of variation equals

a. 0.1125%.

b. 11.25%.

c. 0.20312%.

d. 203.12%.

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Solution

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b

Which of the following scales of measurement are appropriate for quantitative data?

a. Ratio and ordinal

b. Interval and ordinal

c. Interval and ratio

d. Nominal and ordinal

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c

An interviewer has made an error in recording the data. This type of error is known as

a. a non-experimental error.

b. an experimental error.

c. a conglomerate error.

d. a data acquisition error.

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d

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The table above is an example of _____ data.

a. cross-tabulation

b. interval

c. continuous

d. time series

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a

Which of the following variables is quantitative?

a. Phone number

b. Zip code

c. Weight of a package

d. All of these variables are quantitative.

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c

Data measured a nominal scale

a. must be numeric.

b. must be alphabetic.

c. must rank order the data.

d. can be either numeric or nonnumeric.

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d

Which of the following is a categorical variable?

a. Your age on your last birthday

b. Your high school graduation year

c. Your cell phone area code

d. Your accounting class start time

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c

Data collected over several time periods are

a. categorical data.

b. time controlled data.

c. cross-sectional data.

d. time series data.

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d

The scale of measurement that is used to rank order the observation for a variable is called the

a. nominal scale.

b. ordinal scale.

c. ratio scale.

d. interval scale.

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b

In a questionnaire, respondents are asked to mark their gender as male or female. Gender is an example of a(n)

a. quantitative variable.

b. interval-scale variable.

c. categorical variable.

d. ordinal-scale variable.

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c

The collection of all elements of interest in a particular study is

a. descriptive statistics.

b. the population.

c. statistical inference.

d. the sample.

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Solution

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b

The collection of all elements of interest in a particular study is

a. descriptive statistics.

b. the population.

c. statistical inference.

d. the sample.

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Solution

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b

Many data analysts define big data by referring to the three V's of data, which include all of the following except

a. Velocity.

b. Validity.

c. Variety.

d. Volume.

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Solution

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b

How many scales of measurement exist?

a. 8

b. 2

c. 4

d. 6

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Solution

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c

The number of observations will always be the same as the

a. number of variables.

b. number of elements.

c. sample size.

d. population size.

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Solution

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b

The scale of measurement used for variable data that is simply a label for the purpose of identifying the attribute of an element is the

a. ratio scale.

b. interval scale.

c. ordinal scale.

d. nominal scale.

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Solution

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d

Which of the following is not an example of descriptive statistics?

a. Underfilling occurs when a plotted value is between the chart's upper and lower control limits.

b. Underfilling occurs when a plotted value is below the chart's lower control limit.

c. Underfilling occurs when a plotted value is both above the chart's upper and below the chart's lower limits.

d. Underfilling occurs when a plotted value is above the chart's upper control limit.

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b

Ordinary arithmetic operations are meaningful

a. only with quantitative data.

b. with neither quantitative or categorical data.

c. only with categorical data.

d. either with quantitative or categorical data.

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a

Ordinary arithmetic operations are meaningful

a. only with quantitative data.

b. with neither quantitative or categorical data.

c. only with categorical data.

d. either with quantitative or categorical data.

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Solution

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a

A portion of the population selected to represent the population is called

a. statistical inference.

b. a census.

c. descriptive statistics.

d. a sample.

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Solution

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d

Consider the following data summary.

This is an example of a _____.

a. histogram

b. frequency table

c. line graph

d. box plot

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Solution

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a

The subject of data mining deals with

a. keeping data secure so that unauthorized individuals cannot access the data.

b. computational procedure for data analysis.

c. computing the average for data.

d. methods for developing useful decision-making information from large data bases.

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d

A survey to collect data on the entire population is

a. a population.

b. a sample.

c. an inference.

d. a census.

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d

Which of the following is not an example of descriptive statistics?

a. The proportion of mailed-out questionnaires that were returned

b. A histogram depicting the age distribution for 30 randomly selected students

c. A table summarizing the data collected in a sample of new-car buyers

d. An estimate of the number of Alaska residents who have visited Canada

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d

Which of the following disciplines has contributed the least to the development of data mining procedures?

a. Mathematics

b. Statistics

c. Psychology

d. Computer science

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c

In a sample of 800 students in a university, 240 or 30% are Business majors. The 30% is an example of

a. a sample.

b. statistical inference.

c. a population.

d. descriptive statistics.

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d

In a sample of 800 students in a university, 240 or 30% are Business majors. The 30% is an example of

a. a sample.

b. statistical inference.

c. a population.

d. descriptive statistics.

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d

Optimization models, which generate solutions that maximize or minimize some objective subject to a set of constraints, fall into the category of

a. diagnostic analytics.

b. predictive analytics.

c. prescriptive analytics.

d. descriptive analytics.

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c

The process of analyzing sample data in order to draw conclusions about the characteristics of a population is called

a. descriptive statistics.

b. data analysis.

c. data summarization.

d. statistical inference.

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d

Dr. Kurt Thearling, a leading practitioner in the field, defines data mining as "the _________ extraction of _________ information from databases".

a. automated, predictive

b. timely, accurate

c. thorough, insightful

d. intentional, useful

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Solution

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a

Dr. Kurt Thearling, a leading practitioner in the field, defines data mining as "the _________ extraction of _________ information from databases".

a. automated, predictive

b. timely, accurate

c. thorough, insightful

d. intentional, useful

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a

Statistical inference

a. is the same as descriptive statistics.

b. is the same as a census.

c. refers to the process of drawing inferences about the sample based on the characteristics of the population.

d. is the process of drawing inferences about the population based on the information taken from the sample.

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Solution

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d

Data

a. are always numeric.

b. are the raw material of statistics.

c. are always non-numeric.

d. are always categorical.

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b

A population is

a. the collection of all items of interest in a particular study.

b. the same as a sample.

c. the selection of a random sample.

d. always the same size as the sample.

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a

Which of the following is not an example of descriptive statistics?

a. A histogram depicting the age distribution for 30 randomly selected students

b. The proportion of mailed-out questionnaires that were returned

c. An estimate of the number of Alaska residents who have visited Canada

d. A table summarizing the data collected in a sample of new-car buyers

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c

How many scales of measurement exist?

a. 2

b. 4

c. 6

d. 8

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b

A statistics professor asked students in a class their ages. On the basis of this information, the professor states that the average age of all the students in the university is 24 years. This is an example of

a. descriptive statistics.

b. an experiment.

c. statistical inference.

d. a census.

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c

A characteristic of interest for the elements is called a

a. variable.

b. sample.

c. quality.

d. data set.

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a

Data measured a nominal scale

a. must rank order the data.

b. must be alphabetic.

c. must be numeric.

d. can be either numeric or nonnumeric.

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d

Data measured a nominal scale

a. must rank order the data.

b. must be alphabetic.

c. must be numeric.

d. can be either numeric or nonnumeric.

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d

Statistical studies in which researchers control variables of interest are

a. experimental studies.

b. non-experimental studies.

c. control observational studies.

d. observational studies.

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a

In a sample of 1,600 registered voters, 912 or 57% approve of the way the President is doing his job. The 57% approval is an example of

a. descriptive statistics.

b. a population.

c. a sample.

d. statistical inference.

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a

The set of analytical techniques that yield a best course of action is

a. diagnostic analytics.

b. predictive analytics.

c. descriptive analytics.

d. prescriptive analytics.

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d

A sample of 100 individuals in a town was asked how much they paid in property tax per year. On the basis of this information, the reporter states that the average property tax bill of all residents of the town is $1,500. This is an example of _____.

a. descriptive statistics

b. a census

c. an experiment

d. statistical inference

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d

The height of a building, measured in feet, is an example of

a. feet data.

b. categorical data.

c. quantitative data.

d. either categorical or quantitative data.

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c

Optimization models, which generate solutions that maximize or minimize some objective subject to a set of constraints, fall into the category of

a. diagnostic analytics.

b. prescriptive analytics.

c. descriptive analytics.

d. predictive analytics.

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b

The scale of measurement that has an inherent zero value defined is the

a. ratio scale.

b. nominal scale.

c. interval scale.

d. ordinal scale.

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Solution

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a

• Check My Work

Which of the following defines the term "statistics"?

a. Statistics are rarely useful and informative.

b. Statistics refers only to the calculation of numbers, such as a mean.

c. Statistics is the art and science of collecting, analyzing, presenting, and interpreting data.

d. Statistics are used only in sports to calculate "stats" for teams and players such as average rushing yards.

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Solution

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c

• Check My Work

Which of the following defines the term "statistics"?

a. Statistics are rarely useful and informative.

b. Statistics refers only to the calculation of numbers, such as a mean.

c. Statistics is the art and science of collecting, analyzing, presenting, and interpreting data.

d. Statistics are used only in sports to calculate "stats" for teams and players such as average rushing yards.

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Solution

Correct Response

c

• Check My Work

Which of the following defines the term "statistics"?

a. Statistics are rarely useful and informative.

b. Statistics refers only to the calculation of numbers, such as a mean.

c. Statistics is the art and science of collecting, analyzing, presenting, and interpreting data.

d. Statistics are used only in sports to calculate "stats" for teams and players such as average rushing yards.

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Solution

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c

The closing stock price of MNM Corporation for the last 7 trading days is shown below.

Day	Stock Price
1	84
2	87
3	84
4	88
5	85
6	90
7	91

The median is

a. 86.

b. 85.

c. 84.

d. 87.

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d

If the data distribution is symmetric, the skewness is

a. 0.

b. positive.

c. 1.

d. .5.

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a

The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated.

mean = 160	range = 60
mode = 165	variance = 324
median = 170

The coefficient of variation equals

a. 11.25%.

b. 0.1125%.

c. 0.20312%.

d. 203.12%.

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Solution

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a

The value which has half of the observations above it and half the observations below it is called the

a. mean.

b. range.

c. mode.

d. median.

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Solution

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d

Which of the following is not a measure of variability?

a. Range

b. Mode

c. Interquartile range

d. Standard deviation

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b

The closing stock price of MNM Corporation for the last 7 trading days is shown below.

Day	Stock Price
1	84
2	87
3	84
4	88
5	85
6	90
7	91

The mode is

a. 85.

b. 87.

c. 84.

d. 86.

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Solution

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c

The closing stock price of MNM Corporation for the last 7 trading days is shown below.

Day	Stock Price
1	84
2	87
3	84
4	88
5	85
6	90
7	91

The mode is

a. 85.

b. 87.

c. 84.

d. 86.

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Solution

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c

The coefficient of correlation

a. can be larger than 1.

b. cannot be larger than 1.

c. cannot be negative.

d. is the same as the coefficient of determination.

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Solution

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b

Which of the following symbols represents the size of the sample?

a. n

b. σ2

c. σ

d. N

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a

If a negative relationship exists between two variables, x and y, which of the following statements is true?

a. As x decreases, y stays the same.

b. As x decreases, y decreases.

c. As x increases, y decreases.

d. As x increases, y increases.

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c

Data that provide labels or names for categories of like items are known as

a. category data.

b. quantitative data.

c. label data.

d. categorical data.

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d

Consider the scatter diagram below.

What type of relationship is shown for the number of students and their average score?

a. A positive relationship

b. A quadratic relationship

c. No apparent relationship

d. A negative relationship

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Solution

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a

Suppose a sample of 150 individuals was taken. Their gender and their preferred computer manufacturer was noted. Partial results of the study follow in a crosstabulation of column percentages.

If 80 of those in the study prefer Apple computers, how many males preferred Apple computers?

a. 30

b. 80

c. 64

d. 120

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Solution

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c

The numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours	Frequency
0 -9	20
10 - 19	80
20 - 29	200
30 - 39	100

The relative frequency of students working 10 - 19 hours per week is

a. .25

b. .40

c. .80

d. .20

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Solution

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d

A graphical tool typically associated with the display of key performance indicators is a

a. data dashboard.

b. side-by-side bar chart.

c. stem-and-leaf display.

d. stacked bar chart.

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Solution

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a

Which of the following graphical methods shows the relationship between two variables?

a. Crosstabulation

b. Histogram

c. Pie chart

d. Dot plot

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Solution

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a

Which of the following graphical methods shows the relationship between two variables?

a. Crosstabulation

b. Histogram

c. Pie chart

d. Dot plot

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a

Which of the following is a graphical summary of a set of data in which each data value is represented by a dot above the axis?

a. Crosstabulation

b. Histogram

c. Box plot

d. Dot plot

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Solution

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d

The numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours	Frequency
0 -9	20
10 - 19	80
20 - 29	200
30 - 39	100

The cumulative percent frequency for students working less than 20 hours per week is

a. 20%.

b. 80%.

c. 100%.

d. 25%.

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Solution

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d

The numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours	Frequency
0 -9	20
10 - 19	80
20 - 29	200
30 - 39	100

The cumulative percent frequency for students working less than 20 hours per week is

a. 20%.

b. 80%.

c. 100%.

d. 25%.

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Solution

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d

Information on the number of new teachers hired in a school district for each of four years is given in the table below.

The percent frequency of new hires in 2019 is _____.

a. 25%

b. 10%

c. 80%

d. 40%

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Solution

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d

Histograms based on data on housing prices and salaries typically are

a. symmetric.

b. skewed to the right.

c. stacked.

d. skewed to the left.

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Solution

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b

A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.

Undergraduate Major
Graduate School	Business	Engineering	Others	Total
Yes	70	84	126	280
No	182	208	130	520
Total	252	292	256	800

Of those students who are majoring in business, what percentage plans to go to graduate school?

a. 8.75

b. 27.78

c. 72.22

d. 70.00

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b

A graphical tool typically associated with the display of key performance indicators is a

a. stacked bar chart.

b. side-by-side bar chart.

c. data dashboard.

d. stem-and-leaf display.

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Solution

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c

he total number of data items with a value less than the upper limit for the class is given by the

a. relative frequency distribution.

b. cumulative relative frequency distribution.

c. cumulative frequency distribution.

d. frequency distribution.

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c

The relative frequency of a class is

a. equal to the frequency of the class multiplied by 100%.

b. equal to the frequency of the class.

c. always equal to 1%.

d. equal to the frequency of the class divided by the total number of observations, n.

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Solution

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d

The numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours	Frequency
0 - 9	20
10 - 19	80
20 - 29	200
30 - 39	100

The percentage of students who work at least 10 hours per week is

a. 5%.

b. 50%.

c. 100%.

d. 95%.

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Solution

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d

Growth factors for the population of Chattanooga in the past two years have been 8 and 12. The geometric mean has a value of

a. √96.

b. 20.

c. 96.

d. √20.

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Solution

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a

The 75th percentile is referred to as the

a. second quartile.

b. third quartile.

c. fourth quartile.

d. first quartile.

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b

During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperatures of the ten-day period

a. must be at least zero.

b. can be either negative or positive.

c. cannot be computed since all the numbers are negative.

d. is negative since all the numbers are negative.

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Solution

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a

The correlation coefficient

a. is the same as the covariance.

b. can be larger than 1.

c. cannot be less than zero.

d. can be negative.

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Solution

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d

The closing stock price of MNM Corporation for the last 7 trading days is shown below.

Day	Stock Price
1	84
2	87
3	84
4	88
5	85
6	90
7	91

The median is

a. 86.

b. 87.

c. 85.

d. 84.

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Solution

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b

The pth percentile is a value such that approximately

a. p percent of the observations are less than the value and p percent are more than this value.

b. (100 - p) percent of the observations are less than the value and p percent are more than this value.

c. (100 - p) percent of the observations are less than the value and (100 - p) percent are more than this value.

d. p percent of the observations are less than the value and (100 - p) percent are more than this value.

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Solution

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d

In a five number summary, which of the following is not used for data summarization?

a. The largest value

b. The mean

c. The 25th percentile

d. The smallest value

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b

A graphical presentation of the relationship between two quantitative variables is

a. histogram.

b. stem-and-leaf display.

c. scatter diagram.

d. dot plot.

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Solution

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c

A graphical presentation of the relationship between two quantitative variables is

a. histogram.

b. stem-and-leaf display.

c. scatter diagram.

d. dot plot.

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c

Before drawing any conclusions about the relationship between two variables shown in a crosstabulation, you should

a. construct a dot plot and look for significant gaps.

b. construct a scatter diagram and find the trendline.

c. develop a relative frequency distribution.

d. investigate whether any hidden variables could affect the conclusions.

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Solution

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d

Before drawing any conclusions about the relationship between two variables shown in a crosstabulation, you should

a. construct a dot plot and look for significant gaps.

b. construct a scatter diagram and find the trendline.

c. develop a relative frequency distribution.

d. investigate whether any hidden variables could affect the conclusions.

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Solution

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d

Before drawing any conclusions about the relationship between two variables shown in a crosstabulation, you should

a. construct a dot plot and look for significant gaps.

b. construct a scatter diagram and find the trendline.

c. develop a relative frequency distribution.

d. investigate whether any hidden variables could affect the conclusions.

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Solution

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d

Before drawing any conclusions about the relationship between two variables shown in a crosstabulation, you should

a. construct a dot plot and look for significant gaps.

b. construct a scatter diagram and find the trendline.

c. develop a relative frequency distribution.

d. investigate whether any hidden variables could affect the conclusions.

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Solution

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d

A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.

Undergraduate Major
Graduate School	Business	Engineering	Others	Total
Yes	70	84	126	280
No	182	208	130	520
Total	252	292	256	800

Of those students who are majoring in business, what percentage plans to go to graduate school?

a. 72.22

b. 70.00

c. 27.78

d. 8.75

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c

Consider the scatter diagram below.

What type of relationship is shown for the number of students and their average score?

a. A negative relationship

b. No apparent relationship

c. A positive relationship

d. A quadratic relationship

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Solution

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c

When the conclusions based upon the unaggregated data can be completely reversed if we look at the aggregated crosstabulation, the occurrence is known as

a. Reverse correlation.

b. Simpson's paradox.

c. Pareto's rule.

d. Negative correlation.

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Solution

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b

The proper way to construct a stem-and-leaf display for the data set {62, 67, 68, 73, 73, 79, 91, 94, 95, 97} is to

a. include a stem labeled '(8)' and enter no leaves on the stem.

b. include a stem labeled '8' and enter one leaf value of '0' on the stem.

c. include a stem labeled '8' and enter no leaves on the stem.

d. exclude a stem labeled '8.

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Solution

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c

Data that indicate how much or how many are known as

a. quantitative data.

b. categorical data.

c. cumulative data.

d. relative data.

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Solution

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a

The approximate class width for a frequency distribution involving quantitative data can be determined using the expression

a. desired number of classes/class midpoint.

b. mean frequency/total frequency.

c. range/desired number of classes.

d. total frequency/class midpoint.

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Solution

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c

The approximate class width for a frequency distribution involving quantitative data can be determined using the expression

a. desired number of classes/class midpoint.

b. mean frequency/total frequency.

c. range/desired number of classes.

d. total frequency/class midpoint.

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Solution

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c

The approximate class width for a frequency distribution involving quantitative data can be determined using the expression

a. desired number of classes/class midpoint.

b. mean frequency/total frequency.

c. range/desired number of classes.

d. total frequency/class midpoint.

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Solution

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c

The numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours	Frequency
0 - 9	20
10 - 19	80
20 - 29	200
30 - 39	100

The class width used in this frequency distribution is

a. 39.

b. 4.5.

c. 9.

d. 10.

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Solution

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d

A sample of 15 children shows their favorite restaurants:

McDonalds	Luppi's	Mellow Mushroom
Friday's	McDonalds	McDonalds
Pizza Hut	Taco Bell	McDonalds
Mellow Mushroom	Luppi's	Pizza Hut
McDonalds	Friday's	McDonalds

Which of the following distributions would be inappropriate for this data?

a. Relative frequency

b. Frequency

c. Percent frequency

d. Cumulative frequency

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d

In a scatter diagram, a line that provides an approximation of the relationship between the variables is known as a

a. correlation axis.

b. trend line.

c. zero-bias line.

d. determination line.

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Solution

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b

 sample of 15 children shows their favorite restaurants:

McDonalds	Luppi's	Mellow Mushroom
Friday's	McDonalds	McDonalds
Pizza Hut	Taco Bell	McDonalds
Mellow Mushroom	Luppi's	Pizza Hut
McDonalds	Friday's	McDonalds

Which of the following displays is most appropriate for this data?

a. Histogram

b. Stacked bar chart

c. Side-by-side bar chart

d. Pie chart

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Solution

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d

The difference between the lower class limits of adjacent classes provides the

a. class width.

b. class limits.

c. class midpoint.

d. number of classes.

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Solution

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a

The percent frequency of a class is computed by

a. dividing the relative frequency by 100.

b. multiplying the relative frequency by 10.

c. adding 100 to the relative frequency.

d. multiplying the relative frequency by 100.

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d

A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.

Undergraduate Major
Graduate School	Business	Engineering	Others	Total
Yes	70	84	126	280
No	182	208	130	520
Total	252	292	256	800

The above crosstabulation shows

a. frequencies.

b. row percentages.

c. column percentages.

d. overall percentages.

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Solution

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a

The numerical value of the variance

a. is always smaller than the numerical value of the standard deviation.

b. is negative if the mean is negative.

c. is always larger than the numerical value of the standard deviation.

d. can be larger or smaller than the numerical value of the standard deviation.

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d

The numerical value of the variance

a. is always smaller than the numerical value of the standard deviation.

b. is negative if the mean is negative.

c. is always larger than the numerical value of the standard deviation.

d. can be larger or smaller than the numerical value of the standard deviation.

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Solution

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d

Which difficulty of range as a measure of variability is overcome by interquartile range?

a. The sum of the range variances is zero

b. The range is influenced too much by extreme values

c. The range is difficult to compute

d. The range is negative

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b

A box plot is a graphical representation of data that is based on

a. a histogram.

b. z-scores.

c. a five number summary.

d. the empirical rule.

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Solution

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c

What can be concluded from the scatter diagram below for the two variables, years of education and unemployment rate?

a. As years of education increase, the unemployment rate increases; therefore, the correlation coefficient, rxy, will be negative.

b. The correlation coefficient will be equal to zero.

c. As years of education increase, the unemployment rate decreases; therefore, the correlation coefficient, rxy, will be positive.

d. The covariance will be negative.

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Solution

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d

Growth factors for the population of Chattanooga in the past two years have been 8 and 12. The geometric mean has a value of

a. √96.

b. 96.

c. √20.

d. 20.

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Solution

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a

Generally, which one of the following is the least appropriate measure of central tendency for a data set that contains outliers?

a. 50th percentile

b. Median

c. 2nd quartile

d. Mean

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Solution

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d

Generally, which one of the following is the least appropriate measure of central tendency for a data set that contains outliers?

a. 50th percentile

b. Median

c. 2nd quartile

d. Mean

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d

Statements about the proportion of data values that must be within a specified number of standard deviations of the mean can be made using

a. A five-number summary.

b. Percentiles.

c. Chebyshev's theorem.

d. The empirical rule.

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Solution

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c

The relative frequency of a class is computed by

a. dividing the midpoint of the class by the sample size.

b. dividing the frequency of the class by the sample size.

c. dividing the sample size by the frequency of the class.

d. dividing the frequency of the class by the midpoint.

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b

The coefficient of variation is

a. the square of the standard deviation.

b. the same as the variance.

c. the standard deviation divided by the mean times 100.

d. the mean divided by the standard deviation.

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Solution

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c

When a percentage of the smallest and largest values are deleted from a data set, the mean of the remaining data values is the

a. weighted mean.

b. trimmed mean.

c. interquartile mean.

d. geometric mean.

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b

he mean of the sample

a. can never be zero.

b. can never be negative.

c. can assume any value between the highest and the lowest value in the sample.

d. is always smaller than the mean of the population from which the sample was taken.

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Solution

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c

Since the mode is the most frequently occurring data value, it

a. is always larger than the median.

b. is always larger than the mean.

c. can never be larger than the mean.

d. None of these alternatives are correct.

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Solution

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d

The nth root of the product of the n observations is the

a. product variance.

b. weighted mean.

c. geometric mean.

d. product deviation.

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Solution

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c

The numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours	Frequency
0 -9	20
10 - 19	80
20 - 29	200
30 - 39	100

The cumulative percent frequency for students working less than 20 hours per week is

a. 80%.

b. 25%.

c. 20%.

d. 100%.

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Solution

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b

The relative frequency of a class is

a. equal to the frequency of the class divided by the total number of observations, n.

b. equal to the frequency of the class.

c. always equal to 1%.

d. equal to the frequency of the class multiplied by 100%.

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Solution

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a

A sample of 15 children shows their favorite restaurants:

McDonalds	Luppi's	Mellow Mushroom
Friday's	McDonalds	McDonalds
Pizza Hut	Taco Bell	McDonalds
Mellow Mushroom	Luppi's	Pizza Hut
McDonalds	Friday's	McDonalds

Which of the following is the correct relative frequency for McDonalds?

a. .5

b. .6

c. .27

d. .4

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d

If several frequency distributions are constructed from the same data set, the distribution with the widest class width will have the

a. most classes.

b. fewest classes.

c. smallest total frequency.

d. largest total frequency.

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Solution

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b

A display used to compare the frequency, relative frequency or percent frequency of two categorical variables is a

a. stacked bar chart.

b. scatter diagram.

c. pie chart.

d. stem-and-leaf display.

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Solution

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a

A frequency distribution is a tabular summary of data showing the

a. fraction of items in several classes.

b. relative percentage of items in several classes.

c. percentage of items in several classes.

d. number of items in several classes.

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d

When the conclusions based upon the unaggregated data can be completely reversed if we look at the aggregated crosstabulation, the occurrence is known as

a. Pareto's rule.

b. Negative correlation.

c. Simpson's paradox.

d. Reverse correlation.

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Solution

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c

When the conclusions based upon the unaggregated data can be completely reversed if we look at the aggregated crosstabulation, the occurrence is known as

a. Pareto's rule.

b. Negative correlation.

c. Simpson's paradox.

d. Reverse correlation.

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Solution

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c

When the conclusions based upon the unaggregated data can be completely reversed if we look at the aggregated crosstabulation, the occurrence is known as

a. Pareto's rule.

b. Negative correlation.

c. Simpson's paradox.

d. Reverse correlation.

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c

When the conclusions based upon the unaggregated data can be completely reversed if we look at the aggregated crosstabulation, the occurrence is known as

a. Pareto's rule.

b. Negative correlation.

c. Simpson's paradox.

d. Reverse correlation.

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Solution

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c

When the conclusions based upon the unaggregated data can be completely reversed if we look at the aggregated crosstabulation, the occurrence is known as

a. Pareto's rule.

b. Negative correlation.

c. Simpson's paradox.

d. Reverse correlation.

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Solution

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c

When the conclusions based upon the unaggregated data can be completely reversed if we look at the aggregated crosstabulation, the occurrence is known as

a. Pareto's rule.

b. Negative correlation.

c. Simpson's paradox.

d. Reverse correlation.

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Solution

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c

When the conclusions based upon the unaggregated data can be completely reversed if we look at the aggregated crosstabulation, the occurrence is known as

a. Pareto's rule.

b. Negative correlation.

c. Simpson's paradox.

d. Reverse correlation.

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Solution

Correct Response

c

When the conclusions based upon the unaggregated data can be completely reversed if we look at the aggregated crosstabulation, the occurrence is known as

a. Pareto's rule.

b. Negative correlation.

c. Simpson's paradox.

d. Reverse correlation.

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Solution

Correct Response

c

When the conclusions based upon the unaggregated data can be completely reversed if we look at the aggregated crosstabulation, the occurrence is known as

a. Pareto's rule.

b. Negative correlation.

c. Simpson's paradox.

d. Reverse correlation.

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Solution

Correct Response

c

When the conclusions based upon the unaggregated data can be completely reversed if we look at the aggregated crosstabulation, the occurrence is known as

a. Pareto's rule.

b. Negative correlation.

c. Simpson's paradox.

d. Reverse correlation.

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Correct

Solution

Correct Response

c

When the conclusions based upon the unaggregated data can be completely reversed if we look at the aggregated crosstabulation, the occurrence is known as

a. Pareto's rule.

b. Negative correlation.

c. Simpson's paradox.

d. Reverse correlation.

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Correct

Solution

Correct Response

c

When the conclusions based upon the unaggregated data can be completely reversed if we look at the aggregated crosstabulation, the occurrence is known as

a. Pareto's rule.

b. Negative correlation.

c. Simpson's paradox.

d. Reverse correlation.

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Solution

Correct Response

c

The closing stock price of MNM Corporation for the last 7 trading days is shown below.

Day	Stock Price
1	84
2	87
3	84
4	88
5	85
6	90
7	91

The mode is

a. 84.

b. 87.

c. 85.

d. 86.

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Solution

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a

Geometric mean is a measure of

a. variability.

b. dispersion.

c. location.

d. weight.

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Solution

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c

Growth factors for the population of Chattanooga in the past two years have been 8 and 12. The geometric mean has a value of

a. √20.

b. 20.

c. 96.

d. √96.

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Solution

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d

From a population of size 500, a random sample of 50 items is selected. The mode of the sample

a. can be larger, smaller or equal to the mode of the population.

b. must be 500.

c. must be equal to the mean of the population, if the sample is truly random.

d. must be equal to the mode of population, if the sample is truly random.

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Solution

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a

A numerical measure of linear association between two variables is the

a. variance.

b. standard deviation.

c. coefficient of variation.

d. covariance.

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Solution

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d

The geometric mean of 1, 1, 8 is

a. 10.0.

b. 2.0.

c. 3.0.

d. 3.33.

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Solution

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b

Which of the following is not a measure of variability of a single variable?

a. Range

b. Standard deviation

c. Covariance

d. Interquartile range

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Solution

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c

Which of the following is not a measure of variability of a single variable?

a. Range

b. Standard deviation

c. Covariance

d. Interquartile range

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Solution

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c

Which of the following is not a measure of variability of a single variable?

a. Range

b. Standard deviation

c. Covariance

d. Interquartile range

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Solution

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c

Which of the following is not a measure of variability of a single variable?

a. Range

b. Standard deviation

c. Covariance

d. Interquartile range

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Solution

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c

Arithmetic operations provide meaningful results for variables that

a. use any scale of measurement except nominal.

b. are quantitative.

c. appear as non-numerical values.

d. have non-negative values.

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Solution

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b

Which scale of measurement can be either numeric or non-numeric?

a. Nominal

b. Quantitative

c. Interval

d. Ratio

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Solution

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a

Which of the following is a categorical variable?

a. Your age on your last birthday

b. Your accounting class start time

c. Your high school graduation year

d. Your cell phone area code

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Solution

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d

Ordinary arithmetic operations are meaningful

a. either with quantitative or categorical data.

b. only with quantitative data.

c. with neither quantitative or categorical data.

d. only with categorical data.

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Solution

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b

In a sample of 1,600 registered voters, 912 or 57% approve of the way the President is doing his job. A political pollster estimates: "Fifty-seven percent of all voters approve of the President." This statement is an example of

a. statistical inference.

b. a sample.

c. a population.

d. descriptive statistics.

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Solution

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a

A sample of 100 individuals in a town was asked how much they paid in property tax per year. On the basis of this information, the reporter states that the average property tax bill of all residents of the town is $1,500. This is an example of _____.

a. a census

b. statistical inference

c. descriptive statistics

d. an experiment

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Solution

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b

Income is an example of a variable that uses the

a. nominal scale.

b. ordinal scale.

c. interval scale.

d. ratio scale.

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Solution

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d

Income is an example of a variable that uses the

a. nominal scale.

b. ordinal scale.

c. interval scale.

d. ratio scale.

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Solution

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d

Income is an example of a variable that uses the

a. nominal scale.

b. ordinal scale.

c. interval scale.

d. ratio scale.

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Solution

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d

Income is an example of a variable that uses the

a. nominal scale.

b. ordinal scale.

c. interval scale.

d. ratio scale.

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Solution

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d

The proper way to construct a stem-and-leaf display for the data set {62, 67, 68, 73, 73, 79, 91, 94, 95, 97} is to

a. include a stem labeled '8' and enter no leaves on the stem.

b. exclude a stem labeled '8.

c. include a stem labeled '(8)' and enter no leaves on the stem.

d. include a stem labeled '8' and enter one leaf value of '0' on the stem.

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Solution

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a

Which of the following is least useful in making comparisons or showing the relationships of two variables?

a. Stacked bar chart

b. Crosstabulation

c. Scatter diagram

d. Stem-and-leaf display

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Solution

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d

Which of the following is not a recommended guideline for creating an effective graphical display?

a. Give the display a clear and concise title

b. Use three dimensions whenever possible, to give the display depth

c. Label each axis and show the units of measure

d. If colors are used to distinguish categories, use a legend to define them

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b

The relative frequency of a class is

a. equal to the frequency of the class.

b. equal to the frequency of the class multiplied by 100%.

c. always equal to 1%.

d. equal to the frequency of the class divided by the total number of observations, n.

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Solution

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d

A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.

Undergraduate Major
Graduate School	Business	Engineering	Others	Total
Yes	70	84	126	280
No	182	208	130	520
Total	252	292	256	800

Of those students who are majoring in business, what percentage plans to go to graduate school?

a. 8.75

b. 70.00

c. 72.22

d. 27.78

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Solution

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d

A sample of 15 children shows their favorite restaurants:

McDonalds	Luppi's	Mellow Mushroom
Friday's	McDonalds	McDonalds
Pizza Hut	Taco Bell	McDonalds
Mellow Mushroom	Luppi's	Pizza Hut
McDonalds	Friday's	McDonalds

Which of the following is the correct frequency distribution?

a. McDonalds 4, Friday's 3, Pizza Hut 1, Mellow Mushroom 4, Luppi's 3, Taco Bell 1

b. McDonalds 6, Friday's 1, Pizza Hut 3, Mellow Mushroom 1, Luppi's 2, Taco Bell 2

c. McDonalds 6, Friday's 2, Pizza Hut 2, Mellow Mushroom 2, Luppi's 2, Taco Bell 1

d. None of these alternatives are correct.

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Solution

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c

A graphical device for depicting categorical data that have been summarized in a frequency distribution, relative frequency distribution, or percent frequency distribution is a

a. histogram.

b. bar chart.

c. dot plot.

d. stem-and-leaf display.

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Solution

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b

A graphical device for depicting categorical data that have been summarized in a frequency distribution, relative frequency distribution, or percent frequency distribution is a

a. histogram.

b. bar chart.

c. dot plot.

d. stem-and-leaf display.

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Solution

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b

A graphical device for depicting categorical data that have been summarized in a frequency distribution, relative frequency distribution, or percent frequency distribution is a

a. histogram.

b. bar chart.

c. dot plot.

d. stem-and-leaf display.

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Solution

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b

A graphical device for depicting categorical data that have been summarized in a frequency distribution, relative frequency distribution, or percent frequency distribution is a

a. histogram.

b. bar chart.

c. dot plot.

d. stem-and-leaf display.

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Solution

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b

The interquartile range is

a. the difference between the third quartile and the first quartile.

b. the difference between the largest and smallest values.

c. the 50th percentile.

d. another name for the variance.

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Solution

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a

The percentage of data values that must be within one, two, and three standard deviations of the mean for data having a bell-shaped distribution can be determined using

a. Percentiles.

b. A five-number summary.

c. The empirical rule.

d. Chebyshev's theorem.

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Solution

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c

The most frequently occurring value of a data set is called the

a. median.

b. mode.

c. outlier.

d. mean.

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Solution

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b

The most frequently occurring value of a data set is called the

a. median.

b. mode.

c. outlier.

d. mean.

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Solution

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b

The nth root of the product of the n observations is the

a. product variance.

b. weighted mean.

c. product deviation.

d. geometric mean.

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Solution

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d

If the data distribution is symmetric, the skewness is

a. 0.

b. .5.

c. 1.

d. positive.

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a

The value of the sum of the deviations from the mean, i.e., Σ(x-x̄) must always be

a. less than the zero.

b. either positive or negative depending on whether the mean is negative or positive.

c. negative.

d. zero.

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d

The value of the sum of the deviations from the mean, i.e., Σ(x-x̄) must always be

a. less than the zero.

b. either positive or negative depending on whether the mean is negative or positive.

c. negative.

d. zero.

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d

Suppose a sample of 45 measurements gave a data set with a range of –8 to –22. The standard deviation of the measurements

a. must be at least zero.

b. cannot be computed since all the numbers are negative.

c. can be either negative or positive.

d. is negative since all the numbers are negative.

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Solution

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a

Suppose a sample of 45 measurements gave a data set with a range of –8 to –22. The standard deviation of the measurements

a. must be at least zero.

b. cannot be computed since all the numbers are negative.

c. can be either negative or positive.

d. is negative since all the numbers are negative.

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Solution

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a

The owner of a factory regularly requests a graphical summary of all employees' salaries. The graphical summary of salaries is an example of

a. descriptive statistics.

b. an experiment.

c. a sample.

d. statistical inference.

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Solution

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a

Data measured a nominal scale

a. can be either numeric or nonnumeric.

b. must be numeric.

c. must be alphabetic.

d. must rank order the data.

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Solution

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a

A characteristic of interest for the elements is called a

a. sample.

b. data set.

c. quality.

d. variable.

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Solution

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d

Dr. Kurt Thearling, a leading practitioner in the field, defines data mining as "the _________ extraction of _________ information from databases".

a. intentional, useful

b. timely, accurate

c. thorough, insightful

d. automated, predictive

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Solution

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d

Which of the following variables uses the interval scale of measurement?

a. Time duration

b. Standardized test score

c. Vehicle miles-per-gallon

d. Student ID number

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Solution

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b

Statistical studies in which researchers control variables of interest are

a. observational studies.

b. experimental studies.

c. control observational studies.

d. non-experimental studies.

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Solution

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b

An interviewer has made an error in recording the data. This type of error is known as

a. an experimental error.

b. a conglomerate error.

c. a non-experimental error.

d. a data acquisition error.

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Solution

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d

An interviewer has made an error in recording the data. This type of error is known as

a. an experimental error.

b. a conglomerate error.

c. a non-experimental error.

d. a data acquisition error.

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Solution

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d

An interviewer has made an error in recording the data. This type of error is known as

a. an experimental error.

b. a conglomerate error.

c. a non-experimental error.

d. a data acquisition error.

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Solution

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d

The process of capturing, storing, and maintaining data is known as

a. data mining.

b. data warehousing.

c. big data.

d. data manipulation.

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Solution

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b

Income is an example of a variable that uses the

a. ratio scale.

b. interval scale.

c. ordinal scale.

d. nominal scale.

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Solution

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a

Different methods of developing useful information from large data bases are dealt with under

a. data mining.

b. data manipulation.

c. data warehousing.

d. big data.

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Solution

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a

The process of analyzing sample data in order to draw conclusions about the characteristics of a population is called

a. data summarization.

b. descriptive statistics.

c. statistical inference.

d. data analysis.

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Solution

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c

A characteristic of interest for the elements is called a(n) _____.

a. observation

b. variable

c. sample

d. data set

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Solution

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b

Which of the following is not a scale of measurement?

a. Primal

b. Interval

c. Nominal

d. Ordinal

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Solution

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a

The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

a. could not be 22.

b. must be less than 22, since the sample is only a part of the population.

c. must be more than 22, since the population is always larger than the sample.

d. is around 22.

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Solution

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d

The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

a. could not be 22.

b. must be less than 22, since the sample is only a part of the population.

c. must be more than 22, since the population is always larger than the sample.

d. is around 22.

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Solution

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d

The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

a. could not be 22.

b. must be less than 22, since the sample is only a part of the population.

c. must be more than 22, since the population is always larger than the sample.

d. is around 22.

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Solution

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d

The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

a. could not be 22.

b. must be less than 22, since the sample is only a part of the population.

c. must be more than 22, since the population is always larger than the sample.

d. is around 22.

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Solution

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d

The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

a. could not be 22.

b. must be less than 22, since the sample is only a part of the population.

c. must be more than 22, since the population is always larger than the sample.

d. is around 22.

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Solution

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d

The subject of data mining deals with

a. computing the average for data.

b. methods for developing useful decision-making information from large data bases.

c. keeping data secure so that unauthorized individuals cannot access the data.

d. computational procedure for data analysis.

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Solution

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b

The process of capturing, storing, and maintaining data is known as

a. data manipulation.

b. data mining.

c. big data.

d. data warehousing.

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Solution

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d

The number of observations will always be the same as the

a. population size.

b. number of elements.

c. sample size.

d. number of variables.

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Solution

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b

The number of observations will always be the same as the

a. population size.

b. number of elements.

c. sample size.

d. number of variables.

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Solution

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b

The measurement scale suitable for quantitative data is

a. either interval or ratio scale.

b. ordinal scale.

c. nominal scale.

d. only interval scale.

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Solution

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a

On a street, the houses are numbered from 300 to 450. The house numbers are examples of

a. neither quantitative nor categorical data.

b. both quantitative and categorical data.

c. categorical data.

d. quantitative data.

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Solution

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c

How many scales of measurement exist?

a. 6

b. 8

c. 4

d. 2

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Solution

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c

How many scales of measurement exist?

a. 6

b. 8

c. 4

d. 2

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Solution

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c

How many scales of measurement exist?

a. 6

b. 8

c. 4

d. 2

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Solution

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c

Data

a. are the raw material of statistics.

b. are always categorical.

c. are always numeric.

d. are always non-numeric.

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Solution

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a

The sample size

a. is always smaller than the population size.

b. can be larger or smaller than the population size.

c. can be larger than the population size.

d. is always equal to the size of the population.

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Solution

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a

Quantitative data

a. are always numeric.

b. may be either numeric or non-numeric.

c. are never numeric.

d. are always non-numeric.

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Solution

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a

The owner of a factory regularly requests a graphical summary of all employees' salaries. The graphical summary of salaries is an example of

a. statistical inference.

b. an experiment.

c. descriptive statistics.

d. a sample.

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Solution

Correct Response

c

The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

a. is around 22.

b. could not be 22.

c. must be less than 22, since the sample is only a part of the population.

d. must be more than 22, since the population is always larger than the sample.

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Solution

Correct Response

a

The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

a. is around 22.

b. could not be 22.

c. must be less than 22, since the sample is only a part of the population.

d. must be more than 22, since the population is always larger than the sample.

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Solution

Correct Response

a

The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

a. is around 22.

b. could not be 22.

c. must be less than 22, since the sample is only a part of the population.

d. must be more than 22, since the population is always larger than the sample.

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Correct

Solution

Correct Response

a

The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

a. is around 22.

b. could not be 22.

c. must be less than 22, since the sample is only a part of the population.

d. must be more than 22, since the population is always larger than the sample.

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Correct

Solution

Correct Response

a

The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

a. is around 22.

b. could not be 22.

c. must be less than 22, since the sample is only a part of the population.

d. must be more than 22, since the population is always larger than the sample.

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Correct

Solution

Correct Response

a

The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

a. is around 22.

b. could not be 22.

c. must be less than 22, since the sample is only a part of the population.

d. must be more than 22, since the population is always larger than the sample.

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Solution

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a

The largest experimental statistical study ever conducted is believed to be for

a. Polio.

b. Diphtheria.

c. Cholera.

d. Malaria.

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Solution

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a

Which of the following is not a scale of measurement?

a. Ordinal

b. Nominal

c. Primal

d. Interval

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Solution

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c

A hospital has noted that, on average, there are 35 emergency room visits per month in which a child is the patient. The average number of visits is an example of _____.

a. statistical inference

b. a population

c. a descriptive statistic

d. a sample

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Solution

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c

Different methods of developing useful information from large data bases are dealt with under

a. data warehousing.

b. data mining.

c. big data.

d. data manipulation.

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Solution

Correct Response

b

All the data collected in a particular study are referred to as the

a. population.

b. variable.

c. data set.

d. inference.

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Solution

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c

All the data collected in a particular study are referred to as the

a. population.

b. variable.

c. data set.

d. inference.

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Solution

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c

All the data collected in a particular study are referred to as the

a. population.

b. variable.

c. data set.

d. inference.

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Solution

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c

All the data collected in a particular study are referred to as the

a. population.

b. variable.

c. data set.

d. inference.

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Solution

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c

All the data collected in a particular study are referred to as the

a. population.

b. variable.

c. data set.

d. inference.

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Solution

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c

All the data collected in a particular study are referred to as the

a. population.

b. variable.

c. data set.

d. inference.

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Solution

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c

A sample of 15 children shows their favorite restaurants:

McDonalds	Luppi's	Mellow Mushroom
Friday's	McDonalds	McDonalds
Pizza Hut	Taco Bell	McDonalds
Mellow Mushroom	Luppi's	Pizza Hut
McDonalds	Friday's	McDonalds

Which of the following is the correct percent frequency for McDonalds?

a. 10%

b. 27%

c. 2%

d. 40%

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Solution

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d

The number of sick days taken (per month) by 150 factory workers is summarized below.

The cumulative frequency for the class 11–15 is _____.

a. .10

b. .97

c. 145

d. 15

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Solution

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c

For stem-and-leaf displays where the leaf unit is not stated, the leaf unit is assumed to equal

a. -1.

b. 10.

c. 0.

d. 1.

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Solution

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d

The percent frequency of a class is computed by

a. multiplying the relative frequency by 10.

b. dividing the relative frequency by 100.

c. adding 100 to the relative frequency.

d. multiplying the relative frequency by 100.

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Solution

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d

Data that indicate how much or how many are known as

a. relative data.

b. cumulative data.

c. categorical data.

d. quantitative data.

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Solution

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d

Data that indicate how much or how many are known as

a. relative data.

b. cumulative data.

c. categorical data.

d. quantitative data.

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Solution

Correct Response

d

Data that indicate how much or how many are known as

a. relative data.

b. cumulative data.

c. categorical data.

d. quantitative data.

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Solution

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d

Data that indicate how much or how many are known as

a. relative data.

b. cumulative data.

c. categorical data.

d. quantitative data.

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Solution

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d

Data that indicate how much or how many are known as

a. relative data.

b. cumulative data.

c. categorical data.

d. quantitative data.

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Solution

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d

Data that indicate how much or how many are known as

a. relative data.

b. cumulative data.

c. categorical data.

d. quantitative data.

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Solution

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d

Which of the following is not a measure of variability of a single variable?

a. Interquartile range

b. Standard deviation

c. Covariance

d. Range

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Solution

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c

The geometric mean of 1, 2, 4, and 10 is

a. 4.0.

b. 17.0.

c. 2.99.

d. 4.25.

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Solution

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c

The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated.

mean = 160	range = 60
mode = 165	variance = 324
median = 170

The coefficient of variation equals

a. 203.12%.

b. 0.1125%.

c. 11.25%.

d. 0.20312%.

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Solution

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c

The geometric mean of 2, 4, 8 is

a. 4.0.

b. 4.67.

c. 5.0.

d. 16.

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Solution

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a

The geometric mean of 2, 4, 8 is

a. 4.0.

b. 4.67.

c. 5.0.

d. 16.

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Solution

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a

The geometric mean of 2, 4, 8 is

a. 4.0.

b. 4.67.

c. 5.0.

d. 16.

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Solution

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a

The geometric mean of 2, 4, 8 is

a. 4.0.

b. 4.67.

c. 5.0.

d. 16.

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Solution

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a

The geometric mean of 2, 4, 8 is

a. 4.0.

b. 4.67.

c. 5.0.

d. 16.

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Solution

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a

The geometric mean of 2, 4, 8 is

a. 4.0.

b. 4.67.

c. 5.0.

d. 16.

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Solution

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a

The geometric mean of 2, 4, 8 is

a. 4.0.

b. 4.67.

c. 5.0.

d. 16.

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Solution

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a

The geometric mean of 1, 3, 5, and 6 is

a. 3.08.

b. 15.0.

c. 3.75.

d. 5.0.

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Solution

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a

Suppose a sample of 45 measurements gave a data set with a range of –8 to –22. The standard deviation of the measurements

a. can be either negative or positive.

b. cannot be computed since all the numbers are negative.

c. is negative since all the numbers are negative.

d. must be at least zero.

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Solution

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d

From a population of size 500, a random sample of 50 items is selected. The mode of the sample

a. can be larger, smaller or equal to the mode of the population.

b. must be equal to the mode of population, if the sample is truly random.

c. must be equal to the mean of the population, if the sample is truly random.

d. must be 500.

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Solution

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a

The symbol σ is used to represent

a. the standard deviation of the sample.

b. the standard deviation of the population.

c. the variance of the sample.

d. the variance of the population.

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Solution

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b

Geometric mean is a measure of

a. location.

b. weight.

c. variability.

d. dispersion.

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Solution

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a

Geometric mean is a measure of

a. location.

b. weight.

c. variability.

d. dispersion.

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Solution

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a

Geometric mean is a measure of

a. location.

b. weight.

c. variability.

d. dispersion.

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Solution

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a

Geometric mean is a measure of

a. location.

b. weight.

c. variability.

d. dispersion.

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Solution

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a

Geometric mean is a measure of

a. location.

b. weight.

c. variability.

d. dispersion.

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Solution

Correct Response

a

A sample of 15 children shows their favorite restaurants:

McDonalds	Luppi's	Mellow Mushroom
Friday's	McDonalds	McDonalds
Pizza Hut	Taco Bell	McDonalds
Mellow Mushroom	Luppi's	Pizza Hut
McDonalds	Friday's	McDonalds

Which of the following is the correct relative frequency for McDonalds?

a. .5

b. .27

c. .4

d. .6

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Solution

Correct Response

c

A researcher is gathering data from four geographical areas designated: South = 1; North = 2; East = 3; West = 4. The designated geographical regions represent

a. either categorical or quantitative data.

b. categorical data.

c. quantitative data.

d. crosstabular data.

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Solution

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b

The numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours	Frequency
0 - 9	20
10 - 19	80
20 - 29	200
30 - 39	100

The percentage of students who work at least 10 hours per week is

a. 5%.

b. 50%.

c. 100%.

d. 95%.

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Solution

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d

A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.

Undergraduate Major
Graduate School	Business	Engineering	Others	Total
Yes	70	84	126	280
No	182	208	130	520
Total	252	292	256	800

The above crosstabulation shows

a. frequencies.

b. column percentages.

c. overall percentages.

d. row percentages.

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Solution

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a

A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.

Undergraduate Major
Graduate School	Business	Engineering	Others	Total
Yes	70	84	126	280
No	182	208	130	520
Total	252	292	256	800

Of those students who are majoring in business, what percentage plans to go to graduate school?

a. 27.78

b. 8.75

c. 70.00

d. 72.22

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Solution

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a

A graphical device for depicting categorical data that have been summarized in a frequency distribution, relative frequency distribution, or percent frequency distribution is a

a. histogram.

b. dot plot.

c. bar chart.

d. stem-and-leaf display.

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Solution

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c

A graphical device for depicting categorical data that have been summarized in a frequency distribution, relative frequency distribution, or percent frequency distribution is a

a. histogram.

b. dot plot.

c. bar chart.

d. stem-and-leaf display.

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Solution

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c

A graphical device for depicting categorical data that have been summarized in a frequency distribution, relative frequency distribution, or percent frequency distribution is a

a. histogram.

b. dot plot.

c. bar chart.

d. stem-and-leaf display.

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Solution

Correct Response

c

A graphical device for depicting categorical data that have been summarized in a frequency distribution, relative frequency distribution, or percent frequency distribution is a

a. histogram.

b. dot plot.

c. bar chart.

d. stem-and-leaf display.

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Solution

Correct Response

c

A graphical device for depicting categorical data that have been summarized in a frequency distribution, relative frequency distribution, or percent frequency distribution is a

a. histogram.

b. dot plot.

c. bar chart.

d. stem-and-leaf display.

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Solution

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c

In 2000, the average hours of television watched weekly in a household was 5 with a standard deviation of 1.43. In 2002, average hours of television watched weekly in a household was 8 with a standard deviation of 3.12. Which of the following statements is correct?

a. The variance for the number of hours is equal for both years.

b. The number of hours is more variable in the year 2002.

c. The median number of hours of television watched weekly is 6.5.

d. The number of hours is more variable in the year 2000.

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Solution

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b

Which of the following descriptive statistics is not measured in the same units as the data?

a. Standard deviation

b. Variance

c. Interquartile range

d. 35th percentile

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Solution

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b

Since the mode is the most frequently occurring data value, it

a. is always larger than the mean.

b. can never be larger than the mean.

c. is always larger than the median.

d. None of these alternatives are correct.

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Solution

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d

When n-1 is used in the denominator to compute variance,

a. the data set is from a census.

b. the data set is a population.

c. the data set could be either a sample or a population.

d. the data set is a sample.

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Solution

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d

The closing stock price of MNM Corporation for the last 7 trading days is shown below.

Day	Stock Price
1	84
2	87
3	84
4	88
5	85
6	90
7	91

The mode is

a. 85.

b. 87.

c. 84.

d. 86.

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Solution

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c

The closing stock price of MNM Corporation for the last 7 trading days is shown below.

Day	Stock Price
1	84
2	87
3	84
4	88
5	85
6	90
7	91

The mode is

a. 85.

b. 87.

c. 84.

d. 86.

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Solution

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c

The closing stock price of MNM Corporation for the last 7 trading days is shown below.

Day	Stock Price
1	84
2	87
3	84
4	88
5	85
6	90
7	91

The mode is

a. 85.

b. 87.

c. 84.

d. 86.

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Solution

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c

The closing stock price of MNM Corporation for the last 7 trading days is shown below.

Day	Stock Price
1	84
2	87
3	84
4	88
5	85
6	90
7	91

The mode is

a. 85.

b. 87.

c. 84.

d. 86.

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Solution

Correct Response

c

The closing stock price of MNM Corporation for the last 7 trading days is shown below.

Day	Stock Price
1	84
2	87
3	84
4	88
5	85
6	90
7	91

The mode is

a. 85.

b. 87.

c. 84.

d. 86.

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Solution

Correct Response

c

The closing stock price of MNM Corporation for the last 7 trading days is shown below.

Day	Stock Price
1	84
2	87
3	84
4	88
5	85
6	90
7	91

The mode is

a. 85.

b. 87.

c. 84.

d. 86.

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Solution

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c

Which of the following symbols represents the size of the population?

a. σ2

b. μ

c. N

d. σ

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Solution

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c

The correlation coefficient

a. can be larger than 1.

b. can be negative.

c. is the same as the covariance.

d. cannot be less than zero.

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Solution

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b

When computing the mean, the smallest value

a. can never be negative.

b. can never be zero.

c. can never be less than the mean.

d. can be any value.

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Solution

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d

The difference between the largest and the smallest data values is the

a. coefficient of variation.

b. interquartile range.

c. range.

d. variance.

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Solution

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c

The relative frequency of a class is computed by

a. dividing the frequency of the class by n.

b. dividing the cumulative frequency of the class by n.

c. dividing n by cumulative frequency of the class.

d. dividing the frequency of the class by the number of classes.

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Solution

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a

A graphical presentation of the relationship between two quantitative variables is

a. scatter diagram.

b. histogram.

c. dot plot.

d. stem-and-leaf display.

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Solution

Correct Response

a

A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.

Undergraduate Major
Graduate School	Business	Engineering	Others	Total
Yes	70	84	126	280
No	182	208	130	520
Total	252	292	256	800

Of those students who are planning on going to graduate school, what percentage are majoring in engineering?

a. 28.8

b. 30.0

c. 40.4

d. 10.5

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Solution

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b

Data that indicate how much or how many are known as

a. quantitative data.

b. cumulative data.

c. categorical data.

d. relative data.

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Solution

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a

The numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours	Frequency
0 -9	20
10 - 19	80
20 - 29	200
30 - 39	100

The cumulative percent frequency for students working less than 20 hours per week is

a. 20%.

b. 80%.

c. 25%.

d. 100%.

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Solution

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c

A sample of 15 children shows their favorite restaurants:

McDonalds	Luppi's	Mellow Mushroom
Friday's	McDonalds	McDonalds
Pizza Hut	Taco Bell	McDonalds
Mellow Mushroom	Luppi's	Pizza Hut
McDonalds	Friday's	McDonalds

Which of the following displays is most appropriate for this data?

a. Stacked bar chart

b. Histogram

c. Pie chart

d. Side-by-side bar chart

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Solution

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c

In a cumulative frequency distribution, the last class will always have a cumulative frequency equal to

a. one.

b. 10.

c. 100%.

d. the total number of elements in the data set.

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Solution

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d

Data that indicate how much or how many are known as

a. relative data.

b. categorical data.

c. quantitative data.

d. cumulative data.

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Solution

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c

In a stem-and-leaf display,

a. one or more digits are used to define each stem, and a single digit is used to define each leaf.

b. one or more digits are used to define each stem, and one or more digits are used to define each leaf.

c. a single digit is used to define each stem, and a single digit is used to define each leaf.

d. a single digit is used to define each stem, and one or more digits are used to define each leaf.

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Solution

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a

A cumulative relative frequency distribution shows

a. the proportion of data items with values less than or equal to the lower limit of each class.

b. the proportion of data items with values less than or equal to the upper limit of each class.

c. the percentage of data items with values less than or equal to the upper limit of each class.

d. the percentage of data items with values less than or equal to the lower limit of each class.

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Solution

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b

During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperatures of the ten-day period

a. can be either negative or positive.

b. must be at least zero.

c. cannot be computed since all the numbers are negative.

d. is negative since all the numbers are negative.

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Solution

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b

When computing the mean, the smallest value

a. can be any value.

b. can never be zero.

c. can never be negative.

d. can never be less than the mean.

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Solution

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a

If the sample standard deviation for the number of new vehicles sold per month for a sample of 6 car dealerships is 4.2, what is the variance for this set of data?

a. 4.2

b. 17.64

c. 2

d. .7

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Solution

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b

Which of the following symbols represents the standard deviation of the population?

a. σ

b. σ2

c. μ

d. x̄

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Solution

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a

Consider the following data as well as the corresponding stem-and-leaf display on the annual property taxes for eight residents of a city.

What is the leaf unit for the display?

a. 0.1

b. 1

c. 1000

d. 100

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Solution

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d

For stem-and-leaf displays where the leaf unit is not stated, the leaf unit is assumed to equal

a. 0.

b. -1.

c. 10.

d. 1.

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Solution

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d

The relative frequency of a class is computed by

a. dividing the frequency of the class by the midpoint.

b. dividing the midpoint of the class by the sample size.

c. dividing the sample size by the frequency of the class.

d. dividing the frequency of the class by the sample size.

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Solution

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d

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

Hide Feedback

Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

Hide Feedback

Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

Hide Feedback

Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

Hide Feedback

Correct

Solution

Correct Response

a

The number of miles from their residence to their place of work for 120 employees is shown below.

The relative frequency of employees who drive 10 miles or less to work is _____.

a. 0.71

b. 0.85

c. 0.85

d. 0.25

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Correct

Solution

Correct Response

a

In logistic regression,

a. the dependent variable only assumes two continuous values.

b. there are two dependent variables.

c. the dependent variable only assumes two discrete values.

d. there can only be two independent variables.

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Solution

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c

A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function:

Ŷ = 7 - 3x1 + 5x2

For this model, SSR = 3500, SSE = 1500, and the sample size is 18. The adjusted multiple coefficient of determination for this problem is

a. .70.

b. .66.

c. .2289.

d. .8367.

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Solution

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b

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. The multiple coefficient of determination is

a. .68.

b. .42.

c. .32.

d. .50.

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Solution

Correct Response

a

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. At the 5% level, the model

a. is not significant.

b. would be significant if the sample size was larger than 30.

c. is significant.

d. has significant individual parameters.

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c

How many independent variables are there in the estimated regression model ?

a. 1

b. 2

c. 3

d. 4

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d

Which of the following represents the estimated value of the dependent variable(s) in the regression equation ?

a. b0

b. x1, x2, and x3

c. b1, b2, and b3

d.

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d

A measure of identifying the effect of an unusual x value on the regression results is called

a. Cook's D.

b. odd ratio.

c. unusual regression.

d. Leverage.

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d

In a multiple regression model involving 30 observations, the following estimated regression equation was obtained:

Ŷ = 17 + 4x1 - 3x2 + 8x3 + 8x4

For this model, SSR = 700 and SSE = 100. The computed F statistic for testing the significance of the above model is

a. 7.00.

b. 4.00.

c. 50.19.

d. 43.75.

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d

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

	Coefficients	Standard Error
Constant	12.924	4.425
x1	-3.682	2.630
x2	45.216	12.560
Analysis of Variance
Source ofVariation	Degrees of Freedom	Sum ofSquares	MeanSquare	F
Regression		4853	2426.5
Error			485.3

Carry out the test of significance for the parameter β1 at the 1% level. The null hypothesis should

a. be revised to test using F statistic.

b. be tested for β₃ instead.

c. be rejected.

d. not be rejected.

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d

Which of the following does the graph of a multiple regression equation resemble?

a. A nonlinear function in two-dimensional space

b. A two-dimensional line

c. A cylinder in three-dimensional space

d. A plane in three-dimensional space

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d

A logistic regression equation has what shape?

a. Normal

b. Skewed to the left

c. S shape

d. Skewed to the right

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c

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. The estimated income (in $) of a 30-year-old male is

a. $51,000.

b. $21.

c. $51.

d. $90,000.

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a

What values are typically assigned to an indicator variable?

a. there can be any number of dependent variables, but only one independent variable.

b. the multiple coefficient of determination must be larger than 1.

c. the adjusted coefficient of determination can never be negative.

d. there can be several independent variables, but only one dependent variable.

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d

Which of the following would indicate the possible presence of multicollinearity in a regression analysis?

a. A significant p-value for a test of overall significance

b. The F value obtained from the table which is used to test if there is a relationship among the variables at the 5% level equals

c. A small value for the coefficient of determination

d. All of these choices

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b

The mathematical equation that explains how the dependent variable y is related to several independent variables x1, x2, …, xp and the error term ε is

a. a multiple regression equation.

b. a multiple regression model.

c. a simple nonlinear regression model.

d. an estimated multiple regression equation.

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b

In a multiple regression analysis, SSR = 1000 and SSE = 200. The F statistic for this model is

a. 800.

b. 5.

c. 1200.

d. Not enough information is provided to answer this question.

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d

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained.

Ŷ = 29 + 18x1 + 43x2 + 87x3

For this model, SSR = 600 and SSE = 400. The computed F statistic for testing the significance of the above model is

a. .667.

b. .600.

c. 1.50.

d. 20.00.

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d

In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 120 and SSE = 42. The multiple coefficient of determination is

a. .11.

b. .65.

c. .35.

d. .81.

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b

What is the predicted value of y derived from a logistic regression equation with β0 = 0.5, β1 = 0.25, β2 = 1.75, x1 = 5, and x2 = 1?

a. 0.97

b. 0.82

c. 0.94

d. 0.78

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a

In a multiple regression model involving 30 observations, the following estimated regression equation was obtained:

Ŷ = 17 + 4x1 - 3x2 + 8x3 + 8x4

For this model, SSR = 700 and SSE = 100. At the 5% level,

a. it can be concluded that the model is significant.

b. there is no evidence that the model is significant.

c. the conclusion is that the slope of x1 is significant.

d. there is evidence that the slope of x2 is significant.

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a

Which of the following would indicate the possible presence of multicollinearity in a regression analysis?

a. A significant p-value for a test of overall significance

b. A high correlation between two or more independent variables

c. A small value for the coefficient of determination

d. All of these choices

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b

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

	Coefficients	Standard Error
Constant	12.924	4.425
x1	-3.682	2.630
x2	45.216	12.560
Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares	Mean Square	F
Regression		4853	2426.5
Error			485.3

The F value obtained from the table which is used to test if there is a relationship among the variables at the 5% level equals

a. 19.41.

b. 3.63.

c. 3.41.

d. 3.81.

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d

In order to test for the significance of a regression model involving 4 independent variables and 36 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

a. 4 and 32.

b. 4 and 31.

c. 4 and 36.

d. 3 and 35.

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b

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. The test statistic for testing the significance of the model is

a. 1.47.

b. 28.69.

c. .73.

d. 5.22.

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Solution

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b

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. At the 5% level, the model

a. has significant individual parameters.

b. is significant.

c. is not significant.

d. would be significant if the sample size was larger than 30.

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Solution

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b

A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function:

Ŷ = 7 - 3x1 + 5x2

For this model, SSR = 3500, SSE = 1500, and the sample size is 18. The coefficient of x2 indicates that if television advertisement is increased by $1 (holding the unit price constant), sales are expected to

a. increase by $5000.

b. decrease by $2000.

c. increase by $12,000.

d. increase by $5.

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a

The adjusted multiple coefficient of determination is adjusted for the

a. number of independent variables.

b. number of equations.

c. sample size.

d. number of dependent variables.

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a

Which of the following does the graph of a multiple regression equation resemble?

a. A nonlinear function in two-dimensional space

b. A plane in three-dimensional space

c. A cylinder in three-dimensional space

d. A two-dimensional line

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b

In a situation where the dependent variable can assume only one of the two possible discrete values,

a. logistic regression should be applied.

b. there can only be two independent variables.

c. all the independent variables must have values of either zero or one.

d. we must use multiple regression.

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a

A regression analysis was performed to determine the relationship between the costs of a product (y), the time to make the product (x1 ), the number of different materials used (x2), and the amount spent on marketing the product (x3). The estimated regression equation is . What is the estimated cost if the time to make the product is 5 hours, the number of different materials used is 4, and the amount spent on marketing is $100?

a. 205.4

b. 185.4

c. 213

d. 83

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b

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. The yearly income (in $) expected of a 24-year-old male individual is

a. $46,800.

b. $49,800.

c. $13,800.

d. $16,800.

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a

In a multiple regression model, the error term ε is assumed to be a random variable with a mean of

a. zero.

b. 1.

c. any value.

d. -1.

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a

The equation which has the form of E(y) = Ŷ = b0 + b1x1 + b2x2 + ... + bpxp is

a. a multiple nonlinear regression model.

b. an estimated multiple regression equation.

c. a multiple regression equation.

d. an estimated multiple nonlinear regression equation.

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b

In multiple regression analysis, the correlation among the independent variables is termed

a. adjusted coefficient of determination.

b. linearity.

c. adjusted correlation.

d. multicollinearity.

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d

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. The yearly income (in $) expected of a 24-year-old female individual is

a. $19.80.

b. $49,800.

c. $19,800.

d. $49.80.

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Solution

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b

What values are typically assigned to an indicator variable?

a. 0 or 1

b. It depends on the data collected.

c. –1 or 1

d. 1 or 2

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a

In regression analysis, the response variable is the

a. intercept.

b. slope of the regression function.

c. independent variable.

d. dependent variable.

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d

A regression model in which more than one independent variable is used to predict the dependent variable is called

a. a multiple regression model.

b. an adjusted prediction model.

c. a simple linear regression model.

d. an independent model.

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a

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical independent variables in a regression model is called

a. an interaction.

b. a logit variable.

c. a constant variable.

d. a dummy variable.

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d

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

	Coefficients	Standard Error
Constant	12.924	4.425
x1	-3.682	2.630
x2	45.216	12.560
Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares	Mean Square	F
Regression		4853	2426.5
Error			485.3

The degrees of freedom for the sum of squares explained by the regression (SSR) are

a. 3.

b. 15.

c. 13.

d. 2.

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d

For a multiple regression model, SST = 200 and SSE = 50. The multiple coefficient of determination is

a. .80.

b. .25.

c. .75.

d. .33.

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c

The correct relationship between SST, SSR, and SSE is given by

a. n(SST) = p(SSR) + (n - p)(SSE).

b. SSR = SST + SSE.

c. SSE = SSR + SST.

d. SSR = SST - SSE.

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d

What type of model is the regression equation ?

a. It is a first-order model with three predictor variables.

b. It is a third-order model with three predictor variables.

c. It is a fourth-order model with one predictor variable.

d. It is a third-order model with one predictor variable.

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d

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 - 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

If you want to determine whether or not the coefficients of the independent variables are significant, the critical t value at α = .05 is

a. 2.086.

b. 2.064.

c. 2.080.

d. 2.060.

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c

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 - 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

The p-value for testing the significance of the regression model is

a. less than .01.

b. between .01 and .025.

c. greater than .10.

d. between .025 and .05.

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Solution

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a

In multiple regression analysis, the general linear model

a. must contain more than two independent variables.

b. can be used to accommodate curvilinear relationships between the independent variables and dependent variable.

c. cannot be used to accommodate curvilinear relationships between dependent variables and independent variables.

d. cannot use the standard multiple regression procedures for estimation and prediction.

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b

The following regression model

y = β0 + β1x1 + β2x12 + ε

is known as a

a. second-order model with two predictor variables.

b. second-order model with one predictor variable.

c. simple first-order model with one predictor variable.

d. simple first-order model with two predictor variables.

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b

A test used to determine whether or not first-order autocorrelation is present is

a. serial-autocorrelation test.

b. t test.

c. Durbin-Watson Test.

d. chi-square test.

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c

Which of the following values remains the same in the regression analysis for both the full and reduced models?

a. SSR

b. SST

c. SSE

d. All of these choices

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b

Consider the sample correlation coefficients in the table below.

How much of the variability in time can be explained by boxes?

a. .81%

b. 90.2%

c. 66.2%

d. 81.4%

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c

The range of the Durbin-Watson statistic is from

a. -∞ to +∞.

b. 0 to 4.

c. 0 to 1.

d. -1 to 1.

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b

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 - 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

If we are interested in testing for the significance of the relationship among the variables (i.e., significance of the model), the critical value of F at α = .05 is

a. 2.78.

b. 2.76.

c. 3.10.

d. 3.07.

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Solution

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d

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. At the 5% level, the model

a. is significant.

b. is not significant.

c. has significant individual parameters.

d. would be significant if the sample size was larger than 30.

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Solution

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a

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. If we want to test for the significance of the model, the critical value of F at α = .05 is

a. 2.96.

b. 3.33.

c. 3.35.

d. 3.34.

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Solution

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c

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained.

Ŷ = 29 + 18x1 + 43x2 + 87x3

For this model, SSR = 600 and SSE = 400. MSR for this model is

a. 200.

b. 10.

c. 1000.

d. 43.

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Solution

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a

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

	Coefficients	Standard Error
Constant	12.924	4.425
x1	-3.682	2.630
x2	45.216	12.560
Analysis of Variance
Source ofVariation	Degrees of Freedom	Sum ofSquares	MeanSquare	F
Regression		4853	2426.5
Error			485.3

Carry out the test of significance for the parameter β1 at the 1% level. The null hypothesis should

a. not be rejected.

b. be rejected.

c. be revised to test using F statistic.

d. be tested for β₃ instead.

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a

The mathematical equation that explains how the dependent variable y is related to several independent variables x1, x2, …, xp and the error term ε is

a. an estimated multiple regression equation.

b. a simple nonlinear regression model.

c. a multiple regression model.

d. a multiple regression equation.

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Solution

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c

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. The test statistic for testing the significance of the model is

a. .73.

b. 1.47.

c. 5.22.

d. 28.69.

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Solution

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d

A term used to describe the case when the independent variables in a multiple regression model are correlated is

a. leverage.

b. regression.

c. multicollinearity.

d. correlation.

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Solution

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c

What values are typically assigned to an indicator variable?

a. 1 or 2

b. –1 or 1

c. It depends on the data collected.

d. 0 or 1

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Solution

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d

A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares.

SSR = 165

SSE = 60

If we want to test for the significance of the model at a .05 level of significance, the critical F value (from the table) is

a. 3.11.

b. 3.48.

c. 3.34.

d. 3.06.

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Solution

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b

The equation which has the form of E(y) = Ŷ = b0 + b1x1 + b2x2 + ... + bpxp is

a. a multiple nonlinear regression model.

b. an estimated multiple nonlinear regression equation.

c. a multiple regression equation.

d. an estimated multiple regression equation.

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d

When autocorrelation is present, which of the following statements is true?

a. The error terms are related by the function .

b. The error terms are independent.

c. The error terms are normally distributed with mean 0.

d. All of these choices.

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c

Consider the sample correlation coefficients in the table below.

How much of the variability in time can be explained by boxes?

a. 90.2%

b. 81.4%

c. 66.2%

d. .81%

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c

All of the following variable selection procedures are heuristics except

a. backward elimination.

b. stepwise regression.

c. forward selection.

d. best-subsets regression.

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Solution

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d

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 - 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

The test statistic for testing the significance of the model is

a. .73.

b. 3.70.

c. 1.37.

d. 18.93.

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Solution

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d

The variable selection procedure that identifies the best regression model, given a specified number of independent variables, is

a. forward selection.

b. backward elimination.

c. best-subsets regression.

d. stepwise regression.

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c

The following regression model

y = β0 + β1x1 + β2x12 + ε

is known as a

a. second-order model with one predictor variable.

b. simple first-order model with one predictor variable.

c. simple first-order model with two predictor variables.

d. second-order model with two predictor variables.

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a

When autocorrelation is present, one of the assumptions of the regression model is violated and that assumption is

a. the values of the error term ε are independent.

b. the expected value of the error term ε is zero.

c. the values of the error term ε are normally distributed for all values of x.

d. the variance of the error term ε is the same for all values of x.

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Solution

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a

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 - 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

The multiple coefficient of determination is

a. .73.

b. .33.

c. .27.

d. .50.

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Solution

Correct Response

a

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 - 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3= 7
SST = 4800	SSE = 1296

At the 5% level, the coefficient of x2

a. is significant.

b. cannot be tested, because not enough information is provided.

c. should be estimated again, because it is incorrect in the above equation.

d. is not found to be significant.

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Solution

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d

In multiple regression analysis, the general linear model

a. cannot be used to accommodate curvilinear relationships between dependent variables and independent variables.

b. must contain more than two independent variables.

c. cannot use the standard multiple regression procedures for estimation and prediction.

d. can be used to accommodate curvilinear relationships between the independent variables and dependent variable.

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Solution

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d

A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function:

Ŷ = 7 - 3x1 + 5x2

For this model, SSR = 3500, SSE = 1500, and the sample size is 18. The adjusted multiple coefficient of determination for this problem is

a. .70.

b. .66.

c. .8367.

d. .2289.

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Solution

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b

A regression model involved 18 independent variables and 200 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

a. 200 degrees of freedom.

b. 181 degrees of freedom.

c. 199 degrees of freedom.

d. 18 degrees of freedom.

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b

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. If we want to test for the significance of the model, the critical value of F at α = .05 is

a. 3.35.

b. 3.34.

c. 3.33.

d. 2.96.

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Solution

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a

The _______ of an observation is determined by how far the values of the independent variables are from their means.

a. collinearity

b. leverage

c. residual

d. odds ratio

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b

In multiple regression analysis, a variable that cannot be measured in numerical terms is called a

a. categorical independent variable.

b. nonmeasurable random variable.

c. dependent variable.

d. constant variable.

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Solution

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a

A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares.

SSR = 165

SSE = 60

If we want to test for the significance of the model at a .05 level of significance, the critical F value (from the table) is

a. 3.11.

b. 3.06.

c. 3.34.

d. 3.48.

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Solution

Correct Response

d

In a regression model involving more than one independent variable, which of the following tests must be used in order to determine if the relationship between the dependent variable and the set of independent variables is significant?

a. F test

b. chi-square test

c. t test

d. Either a t test or a chi-square test can be used.

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a

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained.

Ŷ = 29 + 18x1 + 43x2 + 87x3

For this model, SSR = 600 and SSE = 400. The computed F statistic for testing the significance of the above model is

a. 20.00.

b. .600.

c. .667.

d. 1.50.

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a

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. The yearly income (in $) expected of a 24-year-old female individual is

a. $49,800.

b. $49.80.

c. $19.80.

d. $19,800.

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a

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

	Coefficients	Standard Error
Constant	12.924	4.425
x1	-3.682	2.630
x2	45.216	12.560
Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares	Mean Square	F
Regression		4853	2426.5
Error			485.3

Carry out the test to determine if there is a relationship among the variables at the 5% level. The null hypothesis should

a. be rejected.

b. be revised to test for multicollinearity.

c. not be rejected.

d. test for individual significance instead.

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a

In multiple regression analysis, the word linear in the term "general linear model" refers to the fact that β0, β1, . . ., βp all have exponents of

a. at least 1.

b. less than 0.

c. 0.

d. 1.

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d

The forward selection procedure starts with _____ independent variable(s) in the multiple regression model.

a. no

b. two

c. all

d. one

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a

When performing a backward elimination procedure, how is the first variable deleted from the model selected?

a. The variable with the largest coefficient for predicting y is selected first.

b. The variable with the smallest standard deviation is selected first.

c. The variable with the highest p-value for the test H0 : βi = 0 is selected first.

d. The variable with the lowest p-value when testing the significance of the coefficients is selected first.

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c

The test statistic for a Durbin–Watson test is d = 1.27 with n = 20 and k = 5. Which of the following conclusions can be made when testing H0: ρ = 0 versus Ha: ρ < 0 at the 1% significance level?

a. There is evidence of negative autocorrelation.

b. There is no evidence of positive autocorrelation.

c. There is no evidence of multicollinearity.

d. There is no evidence of negative autocorrelation.

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d

When dealing with the problem of nonconstant variance, the reciprocal transformation means using

a. 1/x as the independent variable instead of x.

b. 1/y as the dependent variable instead of y.

c. y2 as the dependent variable instead of y.

d. x2 as the independent variable instead of x.

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b

Which of the following is the multiple regression model that would be used to analyze data from a randomized block design with two treatments and four blocks?

a.

b.

c.

d.

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a

Which procedure selects independent variables for inclusion in the model one at a time?

a. Forward selection

b. Backward elimination

c. Logarithm-transformed regression

d. Nonlinear regression

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a

What is the predicted rate ( ) when temperature (x) is 60 for the regression equation  ?

a. 695.68

b. 1506.8

c. 86.8

d. Not enough information is given to compute the predicted rate.

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c

Serial correlation is

a. the correlation between serial numbers of the independent variables.

b. used to identify the effects of multicollinearity.

c. the same as autocorrelation.

d. the same as leverage.

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c

Multicollinearity may cause problems if the absolute value of the sample correlation coefficient for two of the independent variables exceeds what value?

a. .7

b. 1

c. .5

d. .05

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a

If a categorical variable has k levels, the number of dummy variables required is

a. k + 1.

b. k.

c. 2k.

d. k - 1.

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d

In order to test for the significance of a regression model involving 8 independent variables and 121 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

a. 7 and 112.

b. 8 and 121.

c. 8 and 112.

d. 7 and 120.

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c

A regression analysis involved 17 independent variables and 697 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

a. 696 degrees of freedom.

b. 679 degrees of freedom.

c. 714 degrees of freedom.

d. 16 degrees of freedom.

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b

A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function:

Ŷ = 7 - 3x1 + 5x2

For this model, SSR = 3500, SSE = 1500, and the sample size is 18. The multiple coefficient of determination for this problem is

a. .7000.

b. .3040.

c. .2289.

d. .4368.

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a

In multiple regression analysis, a variable that cannot be measured in numerical terms is called a

a. nonmeasurable random variable.

b. dependent variable.

c. constant variable.

d. categorical independent variable.

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d

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

	Coefficients	Standard Error
Constant	12.924	4.425
x1	-3.682	2.630
x2	45.216	12.560
Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares	Mean Square	F
Regression		4853	2426.5
Error			485.3

The interpretation of the coefficient of x1 is that

a. a one unit change in x1 will lead to a 3.682 unit decrease in y.

b. The unit of measurement for y is required to interpret the coefficient.

c. a one unit increase in x1 will lead to a 3.682 unit decrease in y when all other variables are held constant.

d. a one unit increase in x1 will lead to a 3.682 unit decrease in x2 when all other variables are held constant.

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c

What is the predicted value of y derived from a logistic regression equation with β0 = 0.5, β1 = 0.25, β2 = 1.75, x1 = 5, and x2 = 1?

a. 0.97

b. 0.78

c. 0.94

d. 0.82

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a

A measure of goodness of fit for the estimated regression equation is the

a. multicollinearity.

b. multiple coefficient of determination.

c. mean square due to regression.

d. studentized residual.

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b

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. If we want to test for the significance of the model, the critical value of F at α = .05 is

a. 3.35.

b. 3.33.

c. 2.96.

d. 3.34.

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a

Which of the following does the graph of a multiple regression equation resemble?

a. A plane in three-dimensional space

b. A two-dimensional line

c. A nonlinear function in two-dimensional space

d. A cylinder in three-dimensional space

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a

A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares.

SSR = 165

SSE = 60

The test statistic obtained from the information provided is

a. 2.110.

b. 6.875.

c. 5.455.

d. 3.480.

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b

A multiple regression analysis was performed to determine the relationship between the satisfaction rating for a new candy bar and the amount of chocolate used and the amount of caramel used. What is the mean value of the satisfaction rating, if the estimated regression equation is , the amount of chocolate (x1 ) used is 0.35 ounce, and the amount of caramel (x2 ) used is 0.15 ounce?

a. 4.235

b. .50

c. 6.73

d. 8.47

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c

How many independent variables are there in the estimated regression model ?

a. 1

b. 2

c. 3

d. 4

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d

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).

Ŷ = 30 + .7x1 + 3x2

Also provided are SST = 1200 and SSE = 384. If we want to test for the significance of the model, the critical value of F at α = .05 is

a. 2.96.

b. 3.34.

c. 3.35.

d. 3.33.

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c

The equation which has the form of E(y) = Ŷ = b0 + b1x1 + b2x2 + ... + bpxp is

a. a multiple nonlinear regression model.

b. an estimated multiple regression equation.

c. a multiple regression equation.

d. an estimated multiple nonlinear regression equation.

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b

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

	Coefficients	Standard Error
Constant	12.924	4.425
x1	-3.682	2.630
x2	45.216	12.560
Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares	Mean Square	F
Regression		4853	2426.5
Error			485.3

The interpretation of the coefficient of x1 is that

a. a one unit increase in x1 will lead to a 3.682 unit decrease in y when all other variables are held constant.

b. a one unit increase in x1 will lead to a 3.682 unit decrease in x2 when all other variables are held constant.

c. The unit of measurement for y is required to interpret the coefficient.

d. a one unit change in x1 will lead to a 3.682 unit decrease in y.

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a

A logistic regression equation has what shape?

a. Skewed to the right

b. Normal

c. S shape

d. Skewed to the left

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c

In a multiple regression model involving 30 observations, the following estimated regression equation was obtained:

Ŷ = 17 + 4x1 - 3x2 + 8x3 + 8x4

For this model, SSR = 700 and SSE = 100. The computed F statistic for testing the significance of the above model is

a. 50.19.

b. 7.00.

c. 43.75.

d. 4.00.

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c

The mathematical equation that explains how the dependent variable y is related to several independent variables x1, x2, …, xp and the error term ε is

a. a multiple regression model.

b. a multiple regression equation.

c. an estimated multiple regression equation.

d. a simple nonlinear regression model.

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a

If an independent variable is added to a multiple regression model, the R2 value

a. is not affected by the variable added even if it is statistically significant.

b. becomes larger even if the variable added is not statistically significant.

c. becomes larger or smaller depending on the statistical significance of the variable.

d. might or might not become larger even if the variable added is statistically significant.

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b

An example of a first-order model with two predictor variables is

a. y = b0 + b1x1 + ε.

b. y = b0 + b1x1 + b2x2 + ε.

c. y = b0 + b1x2 + ε.

d. y2 = b0 + b1x1 + b2x2 + ε.

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b

In a stepwise regression, which of the following tests is used to determine whether an independent variable makes a significant contribution to the model?

a. F test

b. Chi-square test

c. z test

d. β test

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a

erial correlation is

a. the same as autocorrelation.

b. the same as leverage.

c. the correlation between serial numbers of the independent variables.

d. used to identify the effects of multicollinearity.

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Solution

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a

The correlation in error terms that arises when the error terms at successive points in time are related is termed

a. leverage.

b. autocorrelation.

c. interaction.

d. multicorrelation.

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b

Which of the following statements about the backward elimination procedure is false?

a. It begins with the regression model found using the forward selection procedure.

b. It does not permit an independent variable to be reentered once it has been removed.

c. It does not guarantee that the best regression model will be found.

d. It is a one-variable-at-a-time procedure.

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a

A variable such as z, whose value is z = x1x2, is added to a general linear model in order to account for potential effects of two variables x1 and x2 acting together. This type of effect is

a. called interaction.

b. one of the transformation effects.

c. impossible to occur.

d. called multicollinearity effect.

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a

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 - 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3= 7
SST = 4800	SSE = 1296

At the 5% level, the coefficient of x2

a. is not found to be significant.

b. is significant.

c. cannot be tested, because not enough information is provided.

d. should be estimated again, because it is incorrect in the above equation.

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a

What type of model is the regression equation ?

a. It is a first-order model with three predictor variables.

b. It is a fourth-order model with one predictor variable.

c. It is a third-order model with three predictor variables.

d. It is a third-order model with one predictor variable.

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d

In a stepwise regression, which of the following tests is used to determine whether an independent variable makes a significant contribution to the model?

a. Chi-square test

b. β test

c. F test

d. z test

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c

In order to use the output from a multiple regression analysis to perform the ANOVA test on the difference among the means of three populations, how many dummy variables are needed to indicate treatments?

a. 1

b. 3

c. 4

d. 2

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d

When dealing with the problem of nonconstant variance, the reciprocal transformation means using

a. y2 as the dependent variable instead of y.

b. x2 as the independent variable instead of x.

c. 1/y as the dependent variable instead of y.

d. 1/x as the independent variable instead of x.

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c

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 - 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

If we are interested in testing for the significance of the relationship among the variables (i.e., significance of the model), the critical value of F at α = .05 is

a. 2.76.

b. 3.07.

c. 3.10.

d. 2.78.

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b

When autocorrelation is present, one of the assumptions of the regression model is violated and that assumption is

a. .5

b. .05

c. .7

d. 1

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c

Which of the following tests is used to determine whether an additional variable makes a significant contribution to a multiple regression model?

a. an F test

b. a chi-square test

c. a t test

d. a z test

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a

When autocorrelation is present, one of the assumptions of the regression model is violated and that assumption is

a. the variance of the error term ε is the same for all values of x.

b. the expected value of the error term ε is zero.

c. the values of the error term ε are independent.

d. the values of the error term ε are normally distributed for all values of x.

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c

The correlation in error terms that arises when the error terms at successive points in time are related is termed

a. autocorrelation.

b. leverage.

c. interaction.

d. multicorrelation.

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Solution

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a

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 - 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

At the 5% level, the coefficient of x1

a. is significant.

b. is not found to be significant.

c. should be estimated again, because it is incorrect in the above equation.

d. cannot be tested, because not enough information is provided.

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a

When autocorrelation is present, which of the following statements is true?

a. The error terms are related by the function .

b. The error terms are independent.

c. The error terms are normally distributed with mean 0.

d. All of these choices.

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c

All the independent variables in a multiple regression analysis

a. can be either quantitative or qualitative or both.

b. must assume only positive values.

c. must be quantitative.

d. must be either quantitative or qualitative but not a mix of both.

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a

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 - 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

The test statistic for testing the significance of the model is

a. 3.70.

b. 1.37.

c. 18.93.

d. .73.

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Solution

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c

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 - 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

If you want to determine whether or not the coefficients of the independent variables are significant, the critical t value at α = .05 is

a. 2.060.

b. 2.064.

c. 2.080.

d. 2.086.

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Solution

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c

In a stepwise regression, which of the following tests is used to determine whether an independent variable makes a significant contribution to the model?

a. Chi-square test

b. F test

c. β test

d. z test

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b

Serial correlation is

a. the same as autocorrelation.

b. the same as leverage.

c. the correlation between serial numbers of the independent variables.

d. used to identify the effects of multicollinearity.

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Solution

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a

In order to use the output from a multiple regression analysis to perform the ANOVA test on the difference among the means of three populations, how many dummy variables are needed to indicate treatments?

a. 2

b. 3

c. 1

d. 4

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Solution

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a

The forward selection procedure starts with _____ independent variable(s) in the multiple regression model.

a. no

b. two

c. one

d. all

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a

Which of the following models is not intrinsically linear?

a.

b.

c.

d. All of these models are intrinsically linear.

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d

A regression model involved 5 independent variables and 136 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

a. 135 degrees of freedom.

b. 130 degrees of freedom.

c. 121 degrees of freedom.

d. 4 degrees of freedom.

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b

What is the predicted value of y derived from a logistic regression equation with β0 = 0.5, β1 = 0.25, β2 = 1.75, x1 = 5, and x2 = 1?

a. 0.82

b. 0.94

c. 0.97

d. 0.78

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c

A multiple regression model has the estimated form

Ŷ = 7 + 2x1 + 9x2

As x1 increases by 1 unit (holding x2 constant), y is expected to

a. decrease by 2 units.

b. increase by 9 units.

c. decrease by 9 units.

d. increase by 2 units.

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d

In a multiple regression model involving 30 observations, the following estimated regression equation was obtained:

Ŷ = 17 + 4x1 - 3x2 + 8x3 + 8x4

For this model, SSR = 700 and SSE = 100. The multiple coefficient of determination for the above model is

a. .125.

b. .934.

c. .144.

d. .875.

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Solution

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d

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

	Coefficients	Standard Error
Constant	12.924	4.425
x1	-3.682	2.630
x2	45.216	12.560
Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares	Mean Square	F
Regression		4853	2426.5
Error			485.3

The sum of squares due to error (SSE) equals

a. 4853.

b. 373.31.

c. 485.3.

d. 6308.9.

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d

Using the Durbin-Watson test for negative autocorrelation, we conclude that negative autocorrelation is present if

a. d < dU.

b. d < dL.

c. d > 4 - dL.

d. d < 4 - dU.

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c

What is the predicted profit when the number of items made (x1 ) is 2,500, and the number of stores stocking the product (x2 ) is 5, using the estimated regression equation  ?

a. 1,345

b. 23,200

c. 8,095

d. 75,595

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d

A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares.

SSR = 165

SSE = 60

The multiple coefficient of determination is

a. .275.

b. .7333.

c. .3636.

d. .5.

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b

The null hypothesis in the Durbin-Watson test is always that there is

a. negative autocorrelation.

b. no autocorrelation.

c. either positive or negative autocorrelation.

d. positive autocorrelation.

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b

In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40. The multiple coefficient of determination is

a. .90.

b. .25.

c. .15.

d. .80.

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Solution

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a

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

	Coefficients	Standard Error
Constant	12.924	4.425
x1	-3.682	2.630
x2	45.216	12.560
Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares	Mean Square	F
Regression		4853	2426.5
Error			485.3

We want to test whether the parameter β1 is significant. The test statistic equals

a. -1.4.

b. -5.0.

c. 3.6.

d. 1.4.

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Solution

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a

The following model

y = β0 + β1x1 + ε

is referred to as a

a. curvilinear model.

b. simple first-order model with one predictor variable.

c. simple second-order model with one predictor variable.

d. curvilinear model with one predictor variable.

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Solution

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b

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 - 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

The test statistic for testing the significance of the model is

a. 1.37.

b. 3.70.

c. 18.93.

d. .73.

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Solution

Correct Response

c

Which procedure selects independent variables for inclusion in the model one at a time?

a. Logarithm-transformed regression

b. Backward elimination

c. Forward selection

d. Nonlinear regression

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Solution

Correct Response

c

The joint effect of two independent variables acting together is called

a. transformation.

b. joint regression.

c. autocorrelation.

d. interaction.

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Solution

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d

A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function:

Ŷ = 7 - 3x1 + 5x2

For this model, SSR = 3500, SSE = 1500, and the sample size is 18. To test for the significance of the model, the test statistic F is

a. 17.5.

b. .70.

c. 1.75.

d. 2.33.

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Solution

Correct Response

a

In a multiple regression model involving 30 observations, the following estimated regression equation was obtained:

Ŷ = 17 + 4x1 - 3x2 + 8x3 + 8x4

For this model, SSR = 700 and SSE = 100. The critical F value at α = .05 is

a. 2.99.

b. 2.53.

c. 2.76.

d. 2.69.

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c

The numerical value of the coefficient of determination.

a. is negative if the coefficient of correlation is negative.

b. is always smaller than the coefficient of correlation.

c. can be larger or smaller than the coefficient of correlation.

d. is always larger than the coefficient of correlation.

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c

A regression analysis involved 6 independent variables and 27 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

a. 27 degrees of freedom.

b. 21 degrees of freedom.

c. 26 degrees of freedom.

d. 20 degrees of freedom.

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d

In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed.

Ŷ = 10 - 18x1 + 3x2 + 14x3

Also, the following standard errors and the sum of squares were obtained.

sb1 = 3	sb2 = 6	sb3 = 7
SST = 4800	SSE = 1296

At the .05 level of significance, the coefficient of x3

a. should be estimated again, because it is incorrect in the above equation.

b. cannot be tested, because not enough information is provided.

c. is significant.

d. is not found to be significant.

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d

A model in the form of y = β0 + β1z1 + β2z2 + . . . + βpzp + ε, where each independent variable zj (for j = 1, 2, . . ., p) is a function of x1, x2 , ..., xk, is known as the

a. pth-order z model.

b. general linear model.

c. general curvilinear model.

d. experimental model.

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b

Models in which the parameters have exponents other than 1 are called

a. independent models.

b. autocorrelated models.

c. linear models.

d. nonlinear models.

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d

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

	Coefficients	Standard Error
Constant	12.924	4.425
x1	-3.682	2.630
x2	45.216	12.560
Analysis of Variance
Source of Variation	Degrees of Freedom	Sum of Squares	Mean Square	F
Regression		4853	2426.5
Error			485.3

The t value obtained from the table which is used to test an individual parameter at the 1% level is

a. 2.977.

b. 2.650.

c. 3.012.

d. 2.921.

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c

In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40. The multiple coefficient of determination is

a. .90.

b. .15.

c. .80.

d. .25.

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a

In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

a. 3 and 43.

b. 47 and 3.

c. 2 and 43.

d. 3 and 47.

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a

In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240. The multiple coefficient of determination is

a. .192.

b. .300.

c. .500.

d. .700.

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d

In a multiple regression model, the variance of the error term ε is assumed to be

a. zero.

b. one.

c. the same for all values of the independent variable.

d. the same for all values of the dependent variable.

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c

What is the multiple coefficient of determination for a multiple regression analysis involving 4 independent variables and 240 observations when SST = 870 and SSE = 325?

a. .728

b. .626

c. .374

d. .620

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b

A regression analysis involved 8 independent variables and 99 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

a. 90 degrees of freedom.

b. 97 degrees of freedom.

c. 98 degrees of freedom.

d. 7 degrees of freedom.

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a

Consider the residual plot from the multiple regression analysis to determine the time required to load a truck given the number of boxes to be loaded and the average weight of the boxes.

How many data points in the residual plot given should be investigated further as potential outliers?

a. 0

b. 1

c. 2

d. 3

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c

The ratio of MSR to MSE yields

a. the F statistic.

b. the chi-square statistic.

c. SST.

d. SSR.

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a

 Consider the following hypothesis problem.

n = 30	H0: σ2 = 500
s2 = 625	Ha: σ2 ≠ 500

The test statistic equals

a. 24.00.

b. 36.25.

c. 23.20.

d. 37.50.

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b

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The test statistic is

a. 30.

b. 1.2.

c. 500.

d. 31.2.

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a

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The p-value for this test is

a. less than .10.

b. zero.

c. greater than .10.

d. .05.

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c

Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B.

	Sample A	Sample B
n	11	10
s2	12.1	5

The test statistic for this problem equals

a. 2.

b. 2.42.

c. 1.1.

d. .4132.

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b

The bottler of a certain soft drink claims their equipment to be accurate and that the variance of all filled bottles is .05 or less. The null hypothesis in a test to confirm the claim would be written as

a. H0: σ2 > .05.

b. H0: σ2 ≥ .05.

c. H0: σ2 < .05.

d. H0: σ2 ≤ .05.

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d

Consider the following hypothesis problem.

n = 23	s2 = 60	H0: σ2 ≤ 66
		Ha: σ2 > 66

If the test is to be performed at the .05 level of significance, the null hypothesis

a. should not be tested.

b. should be rejected.

c. should be revised.

d. should not be rejected.

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d

Consider the scenario where

The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the table is(are) _____.

a. 5.629

b. 5.629 and 26.119

c. 6.262 and 27.488

d. 27.488

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b

A sample of 61 observations yielded a sample standard deviation of 6. If we want to test H0: σ2 = 40, the test statistic is

a. 9.

b. 54.90.

c. 54.

d. 9.15.

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c

Given the sample information below, what test statistic should be used to determine whether the standard deviations are equal for two populations, prior to performing a hypothesis test for the equality of the population means?

a. F = 2.49, with numerator degrees of freedom = 29 and denominator degrees of freedom = 19

b. F = 0.40, with degrees of freedom = 19

c. t = 18.75, with degrees of freedom = 19

d. F = 1.58, with numerator degrees of freedom = 19 and denominator degrees of freedom = 29

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a

Consider the following sample information from Population A and Population B.

	Sample A	Sample B
n	24	16
s2	32	38

We want to test the hypothesis that the population variances are equal. The null hypothesis is to be tested at the 10% level of significance. The critical value from the F distribution table is

a. 2.24.

b. 2.11.

c. 2.29.

d. 2.13.

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d

The random variable for a chi-square distribution may assume

a. any value between -1 to 1.

b. any value greater than zero.

c. any value between -∞ to +∞.

d. any negative value.

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b

Consider the following hypothesis problem.

n = 14	H0: σ2 ≤ 410
s = 20	Ha: σ2 > 410

The test statistic equals

a. .63.

b. 13.33.

c. 13.68.

d. 12.68.

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d

The χ 2 value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 20 is _____.

a. 10.851

b. 10.117

c. 30.144

d. 31.410

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c

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The p-value for this test is

a. zero.

b. .05.

c. less than .10.

d. greater than .10.

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d

The sampling distribution used when making inferences about a single population's variance is

a. a t distribution.

b. an F distribution.

c. a chi-square distribution.

d. a normal distribution.

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c

The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the

a. chi-square distribution.

b. normal distribution.

c. t distribution.

d. F distribution.

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d

Consider the following hypothesis problem.

n = 23	s2 = 60	H0: σ2 ≤ 66
		Ha: σ2 > 66

If the test is to be performed at the .05 level of significance, the null hypothesis

a. should not be tested.

b. should be rejected.

c. should not be rejected.

d. should be revised.

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c

We are interested in testing whether the variance of a population is significantly more than 625. The null hypothesis for this test is

a. H0: σ2 > 625.

b. H0: σ2 ≤ 625.

c. H0: σ2 ≥ 625.

d. H0: σ2 ≤ 25.

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b

A sample of 20 bottles of soda yielded a standard deviation of .25 ounce. A 95% confidence interval estimate of the variance for the population is _____.

a. .0361 to .1333

b. –.6378 to .6378

c. .0394 to .1174

d. .0023 to .0083

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a

To avoid the problem of not having access to tables of the F distribution when a one-tailed test is required and with F values given for the lower tail, let the

a. sample variance from the population with the smaller hypothesized variance be the numerator of the test statistic.

b. smaller sample variance be the numerator of the test statistic.

c. larger sample variance be the numerator of the test statistic.

d. sample variance from the population with the larger hypothesized variance be the numerator of the test statistic.

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a

To avoid the problem of not having access to tables of the F distribution when a one-tailed test is required and with F values given for the lower tail, let the

a. smaller sample variance be the numerator of the test statistic.

b. sample variance from the population with the smaller hypothesized variance be the numerator of the test statistic.

c. sample variance from the population with the larger hypothesized variance be the numerator of the test statistic.

d. larger sample variance be the numerator of the test statistic.

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b

The value of F.01 with 9 numerator and 20 denominator degrees of freedom is

a. 2.39.

b. 2.91.

c. 2.94.

d. 3.46.

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d

The chi-square value for a one-tailed (upper tail) hypothesis test at a 5% level of significance and a sample size of 25 is

a. 36.415.

b. 37.652.

c. 33.196.

d. 39.364.

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a

Which of the following rejection rules is proper?

a. Reject H0 if p-value ≥ α/2.

b. Reject H0 if F ≥ Fα.

c. Reject H0 if F ≤ Fα/2.

d. Reject H0 if p-value ≤ Fα.

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b

The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a standard deviation of 4 minutes. A 95% confidence interval estimate for the variance of service times for all their new automobiles is

a. 8.576 to 39.794.

b. 9.46 to 34.09.

c. 2.144 to 9.948.

d. 2.93 to 6.31.

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a

χ2.975 = 8.231 indicates that

a. 97.5% of the chi-square values are less than 8.231.

b. 5% of the chi-square values are equal to 8.231.

c. 2.5% of the chi-square values are greater than 8.231.

d. 97.5% of the chi-square values are greater than 8.231.

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d

Consider the following hypothesis problem.

n = 30	H0: σ2 = 500
s2 = 625	Ha: σ2 ≠ 500

The test statistic equals

a. 36.25.

b. 37.50.

c. 23.20.

d. 24.00.

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a

Consider the following hypothesis problem.

n = 30	H0: σ2 = 500
s2 = 625	Ha: σ2 ≠ 500

At the 5% level of significance, the null hypothesis

a. should be revised.

b. should not be tested.

c. should be rejected.

d. should not be rejected.

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d

The value of F.05 with 8 numerator and 19 denominator degrees of freedom is

a. 2.48.

b. 3.63.

c. 2.96.

d. 2.58.

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a

The symbol used for the variance of the population is

a. σ2.

b. s2.

c. s.

d. σ.

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a

The sampling distribution of the quantity (n - 1)s2/σ2 is the

a. normal distribution.

b. chi-square distribution.

c. F distribution.

d. t distribution.

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b

Which of the following is not a property of a chi-square distribution?

a. χ2 is skewed to the right.

b. The number of degrees of freedom defines the shape of the distribution of χ2.

c. χ2 can have both positive and negative values.

d. All of these choices are properties of the χ2 distribution.

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c

The χ 2 value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 20 is _____.

a. 10.117

b. 10.851

c. 31.410

d. 30.144

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d

Which of the following rejection rules is proper?

a. Reject H0 if p-value ≥ α/2.

b. Reject H0 if p-value ≤ Fα.

c. Reject H0 if F ≤ Fα/2.

d. Reject H0 if F ≥ Fα.

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d

Consider the following hypothesis problem.

n = 23	s2 = 60	H0: σ2 ≤ 66
		Ha: σ2 > 66

If the test is to be performed at the 5% level, the critical value(s) from the chi-square distribution table is(are)

a. 12.338 and 33.924.

b. 12.338.

c. 33.924.

d. 10.982 and 36.781.

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c

A manufacturer of carpentry screws claims that its production machine is very accurate and that the standard deviation of the length of all screws produced is .08 mm or less. A sample of 30 screws showed a standard deviation of .10. The test statistic to test the manufacturer's claim is _____.

a. 18.56

b. 19.2

c. 45.31

d. 23.2

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c

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The test statistic is

a. 1.2.

b. 30.

c. 500.

d. 31.2.

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b

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The number of intervals or categories used to test the hypothesis for this problem is

a. 10.

b. 4.

c. 6.

d. 5.

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c

A study was conducted to examine whether the proportion of females was the same for five groups (Groups A, B, C, D, and E). How many degrees of freedom would the χ2 test statistic have when testing the hypothesis that the proportions in each group are all equal?

a. 0.20

b. 4

c. 5

d. 1

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b

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The calculated value for the test statistic equals

a. 6.

b. 1.67.

c. 2.

d. 0.

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c

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The conclusion of the test at the 5% level of significance is that the

a. distribution is uniform.

b. distribution might have been normal.

c. null hypothesis cannot be rejected.

d. Marascuilo procedure is more applicable.

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a

The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is

a. A chi-square distribution is not used.

b. k – 1.

c. number of rows minus 1 times number of columns minus 1.

d. n – 1.

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c

A population where each of its element is assigned to one and only one of several classes or categories is a

a. Poisson population.

b. multinomial population.

c. binomial population.

d. normal population.

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b

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The expected number of adults who prefer coffee is

a. 200.

b. .25.

c. 150.

d. .33.

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c

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The expected frequency for each group is

a. .333.

b. .50.

c. 50.

d. 100.

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d

Marascuilo procedure is used to test for a significant difference between pairs of population

a. proportions.

b. variances.

c. means.

d. standard deviations.

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a

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. At a .05 level of significance, the null hypothesis

a. cannot be tested.

b. should not be rejected.

c. was designed wrong.

d. should be rejected.

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b

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The calculated value for the test statistic equals

a. 1.67.

b. 0.

c. 6.

d. 2.

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d

Two hundred randomly selected people were asked to state their primary source for news about current events: (1) Television, (2) Radio, (3) Internet, or (4) Other. We wish to determine whether the percent distribution of responses is 10%, 30%, 50%, and 10% for news sources 1 through 4, respectively. What is the null hypothesis?

a. H0: p = .50

b. H0: the proportions are not all equal.

c. H0: p1= .10, p2 = .30, p3 = .50, p4 = .10

d. H0: p1 = .25, p2 = .25, p3 = .25, p4 = .25

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c

The test for goodness of fit

a. is always an upper tail test.

b. is always a lower tail test.

c. can be a lower or an upper tail test.

d. is always a two-tailed test.

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a

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The test statistic for this test of independence is

a. 62.5.

b. 0.

c. 82.5.

d. 8.4.

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a

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The expected frequency for the Business College is

a. 90.

b. .35.

c. 105.

d. .3.

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c

An important application of the chi-square distribution is

a. testing for goodness of fit.

b. testing for the independence of two categorical variables.

c. making inferences about a single population variance.

d. All of these alternatives are correct.

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d

A population where each of its element is assigned to one and only one of several classes or categories is a

a. multinomial population.

b. Poisson population.

c. normal population.

d. binomial population.

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Solution

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a

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The conclusion of the test at the 5% level of significance is that the

a. distribution is uniform.

b. null hypothesis cannot be rejected.

c. Marascuilo procedure is more applicable.

d. distribution might have been normal.

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Solution

Correct Response

a

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. This problem is an example of a

a. z test for proportions.

b. test for independence.

c. multinomial population.

d. Marascuilo procedure.

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c

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The expected frequency of seniors is

a. 68.

b. 60.

c. 64.

d. 20%.

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b

The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies:

Number of Cars Arriving in a 10-Minute Interval	Frequency
0	3
1	10
2	15
3	23
4	30
5	24
6	20
7	13
8	8
9 or more	4
	150

The calculated value for the test statistic equals

a. 1.72.

b. .18.

c. 3.11.

d. 2.89.

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d

Which of the following Chi-Square tests can be used to determine if a data set follows a Normal distribution?

a. Chi Square Test of Association

b. Chi-Square Test of Homogeneity

c. Chi-Square Goodness of Fit

d. Chi-Square Test of Equality of Three or More Population Proportions

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c

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The conclusion of the test at the 5% level of significance is that the

a. Marascuilo procedure is more applicable.

b. distribution might have been normal.

c. distribution is uniform.

d. null hypothesis cannot be rejected.

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Solution

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c

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The expected number of adults who prefer coffee is

a. .33.

b. 200.

c. .25.

d. 150.

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d

Marascuilo procedure is used to test for a significant difference between pairs of population

a. variances.

b. standard deviations.

c. means.

d. proportions.

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d

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The number of intervals or categories used to test the hypothesis for this problem is

a. 5.

b. 6.

c. 10.

d. 4.

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b

With respect to the number of categories, k, when would a multinomial experiment be identical to a binomial experiment?

a. k = 1

b. k = 2

c. k = 3

d. k = 4

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b

An important application of the chi-square distribution is

a. testing for goodness of fit.

b. testing for the independence of two categorical variables.

c. making inferences about a single population variance.

d. All of these alternatives are correct.

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d

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The calculated value for the test statistic equals

a. .01.

b. 4.38.

c. .75.

d. 4.29.

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d

The sampling distribution for a goodness of fit test is the

a. t distribution.

b. chi-square distribution.

c. normal distribution.

d. Poisson distribution.

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b

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The calculated value for the test statistic equals

a. 2.

b. 0.

c. 8.

d. 4.

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c

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

a. 9.348.

b. 5.991.

c. 7.378.

d. 7.815.

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b

If there are three or more populations, then it is

a. impossible to test for equality of the three population proportions, because chi-square tests deal with only two populations.

b. possible to test for equality of three or more population proportions.

c. reasonable to test for equality of multiple population proportions using chi-square lower tail tests.

d. customary to use a t distribution to test for equality of the three population proportions.

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b

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The test statistic for this test of independence is

a. 0.

b. 62.5.

c. 82.5.

d. 8.4.

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b

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The number of degrees of freedom associated with this problem is

a. 299.

b. 300.

c. 2.

d. 3.

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c

The test for goodness of fit

a. is always a two-tailed test.

b. is always an upper tail test.

c. is always a lower tail test.

d. can be a lower or an upper tail test.

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b

Which function in Excel is used to perform a test of independence?

a. CHISQ.TEST

b. T.TEST

c. NORM.S.DIST

d. Z.TEST

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a

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The calculated value for the test statistic equals

a. 0.

b. 2.

c. 1.67.

d. 6.

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b

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The number of intervals or categories used to test the hypothesis for this problem is

a. 10.

b. 6.

c. 5.

d. 4.

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b

A manufacturer of carpentry screws claims that its production machine is very accurate and that the standard deviation of the length of all screws produced is .08 mm or less. A sample of 30 screws showed a standard deviation of .10. The test statistic to test the manufacturer's claim is _____.

a. 18.56

b. 19.2

c. 45.31

d. 23.2

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c

We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is

a. σ2 ≥ 49.

b. σ < 49.

c. σ < 7.

d. σ2 ≥ 7.

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d

The symbol used for the variance of the sample is

a. s2.

b. σ.

c. σ2.

d. s.

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a

The value of F.05 with 8 numerator and 19 denominator degrees of freedom is

a. 2.48.

b. 2.58.

c. 2.96.

d. 3.63.

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a

Which of the following has an F distribution?

a.

b.

c.

d.

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b

A researcher would like to test the hypothesis that population B has a smaller variance than population A, using a 5% level of significance for the hypothesis test. What is the critical value from the F distribution table?

a. 2.39

b. 2.84

c. 2.22

d. 1.96

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c

The 95% confidence interval estimate of a population variance when a sample variance of 324 is obtained from a sample of 81 items is

a. 16.42 to 194.35.

b. 243.086 to 453.520.

c. 254.419 to 429.203.

d. 14.14 to 174.94.

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b

We are interested in testing whether the variance of a population is significantly more than 625. The null hypothesis for this test is

a. H0: σ2 ≤ 625.

b. H0: σ2 > 625.

c. H0: σ2 ≤ 25.

d. H0: σ2 ≥ 625.

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a

For a sample size of 21 at 95% confidence, the chi-square values needed for interval estimation are

a. 10.283 and 35.479.

b. 2.700 and 19.023.

c. 8.260 and 37.566.

d. 9.591 and 34.170.

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d

The producer of a certain medicine claims that their bottling equipment is very accurate and that the standard deviation of all their filled bottles is .1 ounces or less. A sample of 20 bottles showed a standard deviation of .11 ounces. The test statistic to test the claim is

a. 2.3.

b. 22.99.

c. 4.85.

d. 24.2.

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b

The critical value of F using α = .05 when there is a sample size of 21 for the sample with the smaller variance, and there is a sample size of 9 for the sample with the larger sample variance is

a. 2.10.

b. 2.45.

c. 2.94.

d. 2.37.

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b

The chi-square value for a one-tailed (lower tail) test when the level of significance is .1 and the sample size is 15 is

a. 23.685.

b. 7.790.

c. 21.064.

d. 6.571.

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b

Consider the following hypothesis problem.

n = 30	H0: σ2 = 500
s2 = 625	Ha: σ2 ≠ 500

The test statistic equals

a. 37.50.

b. 23.20.

c. 24.00.

d. 36.25.

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d

A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is

a. 100.75.

b. 51.25.

c. 50.

d. 10.

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c

The value of F.05 with 8 numerator and 19 denominator degrees of freedom is

a. 2.48.

b. 2.96.

c. 3.63.

d. 2.58.

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a

χ2.975 = 8.231 indicates that

a. 2.5% of the chi-square values are greater than 8.231.

b. 97.5% of the chi-square values are greater than 8.231.

c. 5% of the chi-square values are equal to 8.231.

d. 97.5% of the chi-square values are less than 8.231.

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b

Consider the following sample information from Population A and Population B.

	Sample A	Sample B
n	24	16
s2	32	38

We want to test the hypothesis that the population variances are equal. The test statistic for this problem equals

a. 1.19.

b. 1.50.

c. .84.

d. .67.

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a

Given the sample information below, what test statistic should be used to determine whether the standard deviations are equal for two populations, prior to performing a hypothesis test for the equality of the population means?

a. t = 18.75, with degrees of freedom = 19

b. F = 1.58, with numerator degrees of freedom = 19 and denominator degrees of freedom = 29

c. F = 2.49, with numerator degrees of freedom = 29 and denominator degrees of freedom = 19

d. F = 0.40, with degrees of freedom = 19

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c

Consider the following hypothesis problem.

n = 23	s2 = 60	H0: σ2 ≤ 66
		Ha: σ2 > 66

The p-value is

a. between .05 and .10.

b. less than .025.

c. between .025 and .05.

d. greater than .10.

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d

The sampling distribution used when making inferences about a single population's variance is

a. a normal distribution.

b. a t distribution.

c. a chi-square distribution.

d. an F distribution.

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c

The value of F.01 with 9 numerator and 20 denominator degrees of freedom is

a. 2.91.

b. 2.94.

c. 2.39.

d. 3.46.

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d

Which of the following is not a property of a chi-square distribution?

a. χ2 is skewed to the right.

b. The number of degrees of freedom defines the shape of the distribution of χ2.

c. χ2 can have both positive and negative values.

d. All of these choices are properties of the χ2 distribution.

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c

A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is

a. 10.

b. 51.25.

c. 50.

d. 100.75.

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c

Which of the following rejection rules is proper?

a. Reject H0 if p-value ≥ α/2.

b. Reject H0 if F ≥ Fα.

c. Reject H0 if F ≤ Fα/2.

d. Reject H0 if p-value ≤ Fα.

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b

In practice, the most frequently encountered hypothesis test about a population variance is a

a. one-tailed test, with rejection region in the lower tail.

b. two-tailed test, with equal-size rejection regions.

c. two-tailed test, with unequal-size rejection regions.

d. one-tailed test, with rejection region in the upper tail.

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d

What is the null hypothesis for testing whether the variance of a population differs from 2.5?

a.

b.

c.

d.

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b

The critical value of F using α = .05 when there is a sample size of 21 for the sample with the smaller variance, and there is a sample size of 9 for the sample with the larger sample variance is

a. 2.45.

b. 2.10.

c. 2.94.

d. 2.37.

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a

Consider the following hypothesis problem.

n = 30	H0: σ2 = 500
s2 = 625	Ha: σ2 ≠ 500

The test statistic equals

a. 24.00.

b. 23.20.

c. 37.50.

d. 36.25.

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d

What is the critical value of F for a one-tailed test at the α=.10 level, when there is a sample size of 8 for the sample with the smaller variance and a sample size of 11 for the sample with the larger sample variance?

a. 2.70

b. 2.41

c. 1.65

d. 3.64

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a

We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is

a. σ2 ≥ 49.

b. σ2 ≥ 7.

c. σ < 7.

d. σ < 49.

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b

Which of the following has a chi-square distribution?

a. (n - 1)s/σ.

b. (n - 1)s2/σ2.

c. (n - 1)σ2/s2.

d. (n - 1)σ/s.

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b

Consider the following hypothesis problem.

n = 23	s2 = 60	H0: σ2 ≤ 66
		Ha: σ2 > 66

The p-value is

a. greater than .10.

b. between .05 and .10.

c. between .025 and .05.

d. less than .025.

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a

The 95% confidence interval estimate of a population variance when a sample variance of 324 is obtained from a sample of 81 items is

a. 16.42 to 194.35.

b. 254.419 to 429.203.

c. 14.14 to 174.94.

d. 243.086 to 453.520.

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d

The value of F.01 with 9 numerator and 20 denominator degrees of freedom is

a. 2.91.

b. 3.46.

c. 2.39.

d. 2.94.

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b

To avoid the problem of not having access to tables of the F distribution when a one-tailed test is required and with F values given for the lower tail, let the

a. sample variance from the population with the smaller hypothesized variance be the numerator of the test statistic.

b. smaller sample variance be the numerator of the test statistic.

c. larger sample variance be the numerator of the test statistic.

d. sample variance from the population with the larger hypothesized variance be the numerator of the test statistic.

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a

The value of F.05 with 8 numerator and 19 denominator degrees of freedom is

a. 2.58.

b. 2.48.

c. 2.96.

d. 3.63.

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b

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. At the .05 level of significance, the null hypothesis

a. should not be tested.

b. should not be rejected.

c. should be rejected.

d. should be revised.

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b

A manufacturer of carpentry screws claims that its production machine is very accurate and that the standard deviation of the length of all screws produced is .08 mm or less. A sample of 30 screws showed a standard deviation of .10. The test statistic to test the manufacturer's claim is _____.

a. 19.2

b. 45.31

c. 23.2

d. 18.56

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b

A sample of 21 observations yielded a sample variance of 16. If we want to test H0: σ2 = 16, the test statistic is

a. 50.

b. 5.

c. 21.

d. 20.

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d

A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square values to be used for this interval estimation are

a. 15.308 and 44.461.

b. 11.808 and 49.645.

c. 16.151 and 40.113.

d. 14.573 and 43.195.

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d

The producer of a certain medicine claims that their bottling equipment is very accurate and that the standard deviation of all their filled bottles is .1 ounces or less. A sample of 20 bottles showed a standard deviation of .11 ounces. The test statistic to test the claim is

a. 2.3.

b. 4.85.

c. 22.99.

d. 24.2.

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c

A sample of 21 observations yielded a sample variance of 16. If we want to test H0: σ2 = 16, the test statistic is

a. 20.

b. 50.

c. 21.

d. 5.

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a

To avoid the problem of not having access to Tables of F distribution when F values are needed for the lower tail, the numerator of the test statistic for a two-tailed test should be the one with

a. the larger sample size.

b. the larger sample variance.

c. the smaller sample variance.

d. the smaller sample size.

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b

Consider the following sample information from Population A and Population B.

	Sample A	Sample B
n	24	16
s2	32	38

We want to test the hypothesis that the population variances are equal. The test statistic for this problem equals

a. 1.19.

b. 1.50.

c. .67.

d. .84.

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Solution

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a

In practice, the most frequently encountered hypothesis test about a population variance is a

a. one-tailed test, with rejection region in the upper tail.

b. one-tailed test, with rejection region in the lower tail.

c. two-tailed test, with unequal-size rejection regions.

d. two-tailed test, with equal-size rejection regions.

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a

A sample of 21 elements is selected to estimate a 90% confidence interval for the variance of the population. The chi-square value(s) to be used for this interval estimation is(are)

a. 12.443 and 28.412.

b. 10.851 and 31.410.

c. 31.410.

d. 12.443.

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b

Consider the following hypothesis problem.

n = 14	H0: σ2 ≤ 410
s = 20	Ha: σ2 > 410

The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the chi-square distribution table is(are)

a. 5.009 and 24.736.

b. 5.629 and 26.119.

c. 23.685.

d. 22.362.

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d

onsider the scenario where

The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the table is(are) _____.

a. 6.262 and 27.488

b. 27.488

c. 5.629 and 26.119

d. 5.629

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c

A sample of 60 items from population 1 has a sample variance of 8 while a sample of 40 items from population 2 has a sample variance of 10. If we want to test whether the variances of the two populations are equal, the test statistic will have a value of

a. 1.56.

b. .8.

c. 1.25.

d. 1.5.

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c

The manager of the service department of a local car dealership has noted that the service times of a sample of 30 new automobiles has a standard deviation of 6 minutes. A 95% confidence interval estimate for the standard deviation of the service times (in minutes) for all their new automobiles is

a. 4.778 to 8.066.

b. 22.833 to 65.059.

c. 16.047 to 45.722.

d. 2.93 to 6.31.

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a

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The calculated value for the test statistic equals

a. 1.66.

b. .65.

c. .54.

d. 6.66.

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a

The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies:

Number of Cars Arriving in a 10-Minute Interval	Frequency
0	3
1	10
2	15
3	23
4	30
5	24
6	20
7	13
8	8
9 or more	4
	150

The p-value is

a. between .05 and .1.

b. greater than .1.

c. between .025 and .05.

d. less than .01.

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b

Which of the following Chi-Square tests can be used to determine if a data set follows a Normal distribution?

a. Chi-Square Goodness of Fit

b. Chi Square Test of Association

c. Chi-Square Test of Equality of Three or More Population Proportions

d. Chi-Square Test of Homogeneity

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a

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The expected number of freshmen is

a. 83.

b. 90.

c. 30.

d. 10.

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b

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The calculated value for the test statistic equals

a. 6.

b. 2.

c. 1.67.

d. 0.

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b

The test for goodness of fit

a. is always an upper tail test.

b. is always a two-tailed test.

c. is always a lower tail test.

d. can be a lower or an upper tail test.

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a

The degrees of freedom for a table with 6 rows and 3 columns is

a. 10.

b. 18.

c. 15.

d. 6.

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a

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. This problem is an example of a

a. z test for proportions.

b. multinomial population.

c. Marascuilo procedure.

d. test for independence.

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b

The number of degrees of freedom associated with the chi-square distribution in a test of independence is

a. number of sample items minus 1.

b. number of populations minus 1.

c. number of populations minus number of estimated parameters minus 1.

d. number of rows minus 1 times number of columns minus 1.

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d

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The expected frequency for each group is

a. .333.

b. 50.

c. .50.

d. 100.

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d

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. With a .05 level of significance, the critical value for the test is

a. 15.507.

b. 7.815.

c. 14.067.

d. 5.991.

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Solution

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b

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The expected number of freshmen is

a. 30.

b. 83.

c. 90.

d. 10.

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c

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The calculated value for the test statistic equals

a. 1.67.

b. 2.

c. 6.

d. 0.

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b

In order not to violate the requirements necessary to use the chi-square distribution for testing equality of three or more population proportions, each expected frequency in a goodness of fit test must be

a. no more than 5.

b. at least 5.

c. less than 2.

d. at least 10.

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b

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The expected frequency for each group is

a. .333.

b. .50.

c. 1/3.

d. 50.

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d

If the sample size is n = 75, what are the degrees of freedom for the appropriate chi-square distribution when testing for independence of two variables each with three categories?

a. 74

b. 4

c. 2

d. 69

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c

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

a. 7.815.

b. 5.991.

c. 7.378.

d. 9.348.

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b

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. At a .05 level of significance, the null hypothesis

a. was designed wrong.

b. should not be rejected.

c. cannot be tested.

d. should be rejected.

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b

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The expected frequency for each group is

a. .333.

b. 50.

c. 100.

d. .50.

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c

A random sample of 550 physicians was selected and classified according to the type of practice they operate and whether or not their practice was full (meaning, not accepting new patients). The counts are given in the table below.

The test statistic for a test of independence is χ2 = 34.893. What is the p-value for this test?

a. p = .004

b. p = .0025

c. p = .05

d. p < .0001

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d

An important application of the chi-square distribution is

a. making inferences about a single population variance.

b. testing for the independence of two categorical variables.

c. testing for goodness of fit.

d. All of these alternatives are correct.

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d

How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?

a. 7

b. 62

c. 9

d. 74

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c

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The expected frequency for each group is

a. .50.

b. .333.

c. 100.

d. 50.

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c

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The expected number of adults who prefer coffee is

a. 150.

b. .25.

c. .33.

d. 200.

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a

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The test statistic for this test of independence is

a. 0.

b. 8.4.

c. 82.5.

d. 62.5.

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Solution

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d

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. This problem is an example of a

a. z test for proportions.

b. test for independence.

c. Marascuilo procedure.

d. multinomial population.

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d

The degrees of freedom for a data table with 10 rows and 11 columns is

a. 90.

b. 21.

c. 100.

d. 110.

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a

If there are three or more populations, then it is

a. impossible to test for equality of the three population proportions, because chi-square tests deal with only two populations.

b. customary to use a t distribution to test for equality of the three population proportions.

c. reasonable to test for equality of multiple population proportions using chi-square lower tail tests.

d. possible to test for equality of three or more population proportions.

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d

The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies:

Number of Cars Arriving in a 10-Minute Interval	Frequency
0	3
1	10
2	15
3	23
4	30
5	24
6	20
7	13
8	8
9 or more	4
	150

The calculated value for the test statistic equals

a. 1.72.

b. 3.11.

c. .18.

d. 2.89.

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Solution

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d

The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies:

Number of Cars Arriving in a 10-Minute Interval	Frequency
0	3
1	10
2	15
3	23
4	30
5	24
6	20
7	13
8	8
9 or more	4
	150

The p-value is

a. less than .01.

b. between .025 and .05.

c. greater than .1.

d. between .05 and .1.

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c

If there are three or more populations, then it is

a. possible to test for equality of three or more population proportions.

b. impossible to test for equality of the three population proportions, because chi-square tests deal with only two populations.

c. customary to use a t distribution to test for equality of the three population proportions.

d. reasonable to test for equality of multiple population proportions using chi-square lower tail tests.

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a

The degrees of freedom for a table with 6 rows and 3 columns is

a. 10.

b. 6.

c. 15.

d. 18.

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a

In order not to violate the requirements necessary to use the chi-square distribution for testing equality of three or more population proportions, each expected frequency in a goodness of fit test must be

a. at least 5.

b. no more than 5.

c. at least 10.

d. less than 2.

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Solution

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a

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The calculated value for the test statistic equals

a. 2.

b. 20.

c. -2.

d. 4.

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d

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The p-value is

a. between .05 and .1.

b. less than .005.

c. between .025 and .05.

d. greater than .1.

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d

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

At the 5% level of significance, the conclusion of the test is that the

a. data does not follow a normal distribution.

b. sample data is incorrect.

c. null hypothesis cannot be rejected.

d. sample data has no probability distribution.

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c

Which function in Excel is used to perform a test of independence?

a. Z.TEST

b. CHISQ.TEST

c. T.TEST

d. NORM.S.DIST

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b

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a

a. probability test.

b. comparison test.

c. goodness of fit test.

d. normality test.

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Solution

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c

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. This problem is an example of a

a. multinomial population.

b. test for independence.

c. Marascuilo procedure.

d. z test for proportions.

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a

The number of categorical outcomes per trial for a multinomial probability distribution is

a. four or more.

b. two or more.

c. three or more.

d. five or more.

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c

If there are three or more populations, then it is

a. reasonable to test for equality of multiple population proportions using chi-square lower tail tests.

b. impossible to test for equality of the three population proportions, because chi-square tests deal with only two populations.

c. possible to test for equality of three or more population proportions.

d. customary to use a t distribution to test for equality of the three population proportions.

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c

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The expected frequency for each group is

a. 1/3.

b. .50.

c. 50.

d. .333.

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c

The properties of a multinomial experiment include all of the following except

a. the experiment consists of a sequence of n identical trials.

b. the probability of each outcome can change from trial to trial.

c. the trials are independent.

d. three or more outcomes are possible on each trial.

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b

In order not to violate the requirements necessary to use the chi-square distribution for testing equality of three or more population proportions, each expected frequency in a goodness of fit test must be

a. less than 2.

b. at least 10.

c. no more than 5.

d. at least 5.

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d

A random sample of 100 high school students was surveyed regarding their favorite subject. The following counts were obtained:

The researcher conducted a test to determine whether the proportion of students was equal for all four subjects. What is the value of the test statistic?

a. 25

b. 6

c. 0

d. –4

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b

The test statistic for goodness of fit has a chi-square distribution with k - 1 degrees of freedom provided that the expected frequencies for all categories are

a. 5 or more.

b. 10 or more.

c. 2k.

d. k or more.

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Solution

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a

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. With a .05 level of significance, the critical value for the test is

a. 5.991.

b. 15.507.

c. 14.067.

d. 7.815.

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Solution

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d

Marascuilo procedure is used to test for a significant difference between pairs of population

a. proportions.

b. means.

c. variances.

d. standard deviations.

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Solution

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a

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The conclusion of the test at the 5% level of significance is that the

a. Marascuilo procedure is more applicable.

b. distribution is uniform.

c. distribution might have been normal.

d. null hypothesis cannot be rejected.

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Solution

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b

The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies:

Number of Cars Arriving in a 10-Minute Interval	Frequency
0	3
1	10
2	15
3	23
4	30
5	24
6	20
7	13
8	8
9 or more	4
	150

The p-value is

a. between .05 and .1.

b. between .025 and .05.

c. less than .01.

d. greater than .1.

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Solution

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d

Given the sample information below, what test statistic should be used to determine whether the standard deviations are equal for two populations, prior to performing a hypothesis test for the equality of the population means?

a. t = 18.75, with degrees of freedom = 19

b. F = 0.40, with degrees of freedom = 19

c. F = 1.58, with numerator degrees of freedom = 19 and denominator degrees of freedom = 29

d. F = 2.49, with numerator degrees of freedom = 29 and denominator degrees of freedom = 19

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d

A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is

a. 50.

b. 100.75.

c. 51.25.

d. 10.

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a

In practice, the most frequently encountered hypothesis test about a population variance is a

a. one-tailed test, with rejection region in the upper tail.

b. two-tailed test, with equal-size rejection regions.

c. two-tailed test, with unequal-size rejection regions.

d. one-tailed test, with rejection region in the lower tail.

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a

A sample of 21 observations yielded a sample variance of 16. If we want to test H0: σ2 = 16, the test statistic is

a. 21.

b. 5.

c. 50.

d. 20.

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d

Consider the following hypothesis problem.

n = 14	H0: σ2 ≤ 410
s = 20	Ha: σ2 > 410

At the 5% level of significance, the null hypothesis

a. should not be rejected.

b. should be revised.

c. should be rejected.

d. should not be tested.

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a

The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the

a. chi-square distribution.

b. normal distribution.

c. F distribution.

d. t distribution.

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c

The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the

a. chi-square distribution.

b. normal distribution.

c. F distribution.

d. t distribution.

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c

We are interested in testing whether the variance of a population is significantly more than 625. The null hypothesis for this test is

a. H0: σ2 ≥ 625.

b. H0: σ2 ≤ 625.

c. H0: σ2 ≤ 25.

d. H0: σ2 > 625.

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b

Which of the following has an F distribution?

a. s1/s2.

b. (n - 1)s1/s2.

c. (n - 1)s/σ.

d. s12/s22.

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d

Which of the following has an F distribution?

a. s1/s2.

b. (n - 1)s1/s2.

c. (n - 1)s/σ.

d. s12/s22.

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d

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The expected number of adults who prefer coffee is

a. .33.

b. 150.

c. .25.

d. 200.

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Solution

Correct Response

b

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a

a. goodness of fit test.

b. normality test.

c. comparison test.

d. probability test.

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Solution

Correct Response

a

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The calculated value for the test statistic equals

a. .54.

b. 6.66.

c. .65.

d. 1.66.

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Solution

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d

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The number of degrees of freedom associated with this problem is

a. 299.

b. 300.

c. 3.

d. 2.

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d

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The expected frequency for the Business College is

a. .3.

b. 90.

c. .35.

d. 105.

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d

Which function in Excel is used to perform a test of independence?

a. T.TEST

b. Z.TEST

c. NORM.S.DIST

d. CHISQ.TEST

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Solution

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d

An important application of the chi-square distribution is

a. making inferences about a single population variance.

b. testing for goodness of fit.

c. testing for the independence of two categorical variables.

d. All of these alternatives are correct.

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Solution

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d

How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?

a. 62

b. 7

c. 9

d. 74

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c

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The p-value is

a. between .025 and .05.

b. less than .005.

c. greater than .1.

d. between .05 and .1.

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c

The 99% confidence interval estimate for a population variance when a sample standard deviation of 12 is obtained from a sample of 10 items is

a. 4.589 to 62.253.

b. 54.941 to 746.974.

c. 62.042 to 562.895.

d. 46.538 to 422.171.

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b

A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: σ2 = 20, the test statistic is

a. 50.

b. 10.

c. 51.25.

d. 100.75.

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Solution

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a

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. At the .05 level of significance, the null hypothesis

a. should be revised.

b. should not be rejected.

c. should be rejected.

d. should not be tested.

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b

We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is

a. H0: σ2 < 1.44.

b. H0: σ < 1.20.

c. H0: σ2 ≥ 1.44.

d. H0: s2 ≥ 1.44.

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c

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The p-value for this test is

a. less than .10.

b. zero.

c. .05.

d. greater than .10.

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Solution

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d

The contents of a sample of 26 cans of apple juice showed a standard deviation of .06 ounces. We are interested in testing whether the variance of the population is significantly more than .003. The p-value for this test is

a. less than .10.

b. zero.

c. .05.

d. greater than .10.

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Solution

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d

Consider the following sample information from Population A and Population B.

	Sample A	Sample B
n	24	16
s2	32	38

We want to test the hypothesis that the population variances are equal. The null hypothesis is to be tested at the 10% level of significance. The critical value from the F distribution table is

a. 2.11.

b. 2.29.

c. 2.13.

d. 2.24.

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c

Which of the following rejection rules is proper?

a. Reject H0 if p-value ≥ α/2.

b. Reject H0 if F ≤ Fα/2.

c. Reject H0 if p-value ≤ Fα.

d. Reject H0 if F ≥ Fα.

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d

Which of the following rejection rules is proper?

a. Reject H0 if p-value ≥ α/2.

b. Reject H0 if F ≤ Fα/2.

c. Reject H0 if p-value ≤ Fα.

d. Reject H0 if F ≥ Fα.

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d

Which of the following rejection rules is proper?

a. Reject H0 if p-value ≥ α/2.

b. Reject H0 if F ≤ Fα/2.

c. Reject H0 if p-value ≤ Fα.

d. Reject H0 if F ≥ Fα.

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d

Which of the following is not a property of a chi-square distribution?

a. χ2 is skewed to the right.

b. The number of degrees of freedom defines the shape of the distribution of χ2.

c. χ2 can have both positive and negative values.

d. All of these choices are properties of the χ2 distribution.

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c

χ2.975 = 8.231 indicates that

a. 97.5% of the chi-square values are less than 8.231.

b. 5% of the chi-square values are equal to 8.231.

c. 97.5% of the chi-square values are greater than 8.231.

d. 2.5% of the chi-square values are greater than 8.231.

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c

The 95% confidence interval estimate of a population variance when a sample variance of 324 is obtained from a sample of 81 items is

a. 254.419 to 429.203.

b. 16.42 to 194.35.

c. 14.14 to 174.94.

d. 243.086 to 453.520.

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d

We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is

a. σ2 ≥ 7.

b. σ < 7.

c. σ < 49.

d. σ2 ≥ 49.

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a

The chi-square value for a one-tailed (upper tail) hypothesis test at a 5% level of significance and a sample size of 25 is

a. 36.415.

b. 39.364.

c. 37.652.

d. 33.196.

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a

There is a .90 probability of obtaining a χ2 value such that

a. χ2.90 < χ2 < χ2.10

b. χ2.05 < χ2 < χ2.95

c. χ2.10 ≤ χ2 ≤ χ2.90

d. χ2.95 ≤ χ2 ≤ χ2.05

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d

Consider the following sample information from Population A and Population B.

	Sample A	Sample B
n	24	16
s2	32	38

We want to test the hypothesis that the population variances are equal. At the 10% level of significance, the null hypothesis

a. should be revised.

b. should be rejected.

c. should not be tested.

d. should not be rejected.

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d

Consider the following hypothesis problem.

n = 14	H0: σ2 ≤ 410
s = 20	Ha: σ2 > 410

The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the chi-square distribution table is(are)

a. 23.685.

b. 22.362.

c. 5.009 and 24.736.

d. 5.629 and 26.119.

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b

Consider the following hypothesis problem.

n = 14	H0: σ2 ≤ 410
s = 20	Ha: σ2 > 410

The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the chi-square distribution table is(are)

a. 23.685.

b. 22.362.

c. 5.009 and 24.736.

d. 5.629 and 26.119.

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b

Consider the following hypothesis problem.

n = 14	H0: σ2 ≤ 410
s = 20	Ha: σ2 > 410

The null hypothesis is to be tested at the 5% level of significance. The critical value(s) from the chi-square distribution table is(are)

a. 23.685.

b. 22.362.

c. 5.009 and 24.736.

d. 5.629 and 26.119.

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b

A sample of 21 observations yielded a sample variance of 16. If we want to test H0: σ2 = 16, the test statistic is

a. 5.

b. 50.

c. 21.

d. 20.

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d

The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a standard deviation of 4 minutes. A 95% confidence interval estimate for the variance of service times for all their new automobiles is

a. 8.576 to 39.794.

b. 2.144 to 9.948.

c. 2.93 to 6.31.

d. 9.46 to 34.09.

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a

We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is

a. H0: σ < 1.20.

b. H0: s2 ≥ 1.44.

c. H0: σ2 < 1.44.

d. H0: σ2 ≥ 1.44.

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d

The χ 2 value for a one-tailed (upper tail) hypothesis test at 95% confidence and a sample size of 20 is _____.

a. 31.410

b. 10.851

c. 10.117

d. 30.144

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d

Consider the following hypothesis problem.

n = 30	H0: σ2 = 500
s2 = 625	Ha: σ2 ≠ 500

At the 5% level of significance, the null hypothesis

a. should not be tested.

b. should be rejected.

c. should not be rejected.

d. should be revised.

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c

What is the critical value of F for a one-tailed test at the α=.10 level, when there is a sample size of 8 for the sample with the smaller variance and a sample size of 11 for the sample with the larger sample variance?

a. 1.65

b. 3.64

c. 2.70

d. 2.41

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c

What is the null hypothesis for testing whether the variance of a population differs from 2.5?

a.

b.

c.

d.

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a

What is the null hypothesis for testing whether the variance of a population differs from 2.5?

a.

b.

c.

d.

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a

What is the null hypothesis for testing whether the variance of a population differs from 2.5?

a.

b.

c.

d.

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a

What is the null hypothesis for testing whether the variance of a population differs from 2.5?

a.

b.

c.

d.

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a

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

At the 5% level of significance, the conclusion of the test is that the

a. sample data has no probability distribution.

b. null hypothesis cannot be rejected.

c. data does not follow a normal distribution.

d. sample data is incorrect.

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b

A random sample of 550 physicians was selected and classified according to the type of practice they operate and whether or not their practice was full (meaning, not accepting new patients). The counts are given in the table below.

The test statistic for a test of independence is χ2 = 34.893. What is the p-value for this test?

a. p = .05

b. p = .0025

c. p < .0001

d. p = .004

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c

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a

a. comparison test.

b. normality test.

c. goodness of fit test.

d. probability test.

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c

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The calculated value for the test statistic equals

a. 2.

b. 6.

c. 1.67.

d. 0.

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a

How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?

a. 62

b. 9

c. 74

d. 7

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b

A population where each of its element is assigned to one and only one of several classes or categories is a

a. normal population.

b. multinomial population.

c. binomial population.

d. Poisson population.

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b

The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies:

Number of Cars Arriving in a 10-Minute Interval	Frequency
0	3
1	10
2	15
3	23
4	30
5	24
6	20
7	13
8	8
9 or more	4
	150

The calculated value for the test statistic equals

a. .18.

b. 2.89.

c. 3.11.

d. 1.72.

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b

If there are three or more populations, then it is

a. possible to test for equality of three or more population proportions.

b. impossible to test for equality of the three population proportions, because chi-square tests deal with only two populations.

c. reasonable to test for equality of multiple population proportions using chi-square lower tail tests.

d. customary to use a t distribution to test for equality of the three population proportions.

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a

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The expected number of adults who prefer coffee is

a. 200.

b. .25.

c. .33.

d. 150.

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d

The table below gives beverage preferences for random samples of teens and adults.

	Teens	Adults	Total
Coffee	50	200	250
Tea	100	150	250
Soft Drink	200	200	400
Other	50	50	100
	400	600	1000

We are asked to test for independence between age (i.e., adult and teen) and drink preferences. The expected number of adults who prefer coffee is

a. 200.

b. .25.

c. .33.

d. 150.

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d

Two hundred randomly selected people were asked to state their primary source for news about current events: (1) Television, (2) Radio, (3) Internet, or (4) Other. We wish to determine whether the percent distribution of responses is 10%, 30%, 50%, and 10% for news sources 1 through 4, respectively. What is the null hypothesis?

a. H0: the proportions are not all equal.

b. H0: p1= .10, p2 = .30, p3 = .50, p4 = .10

c. H0: p1 = .25, p2 = .25, p3 = .25, p4 = .25

d. H0: p = .50

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b

The test for goodness of fit

a. can be a lower or an upper tail test.

b. is always a lower tail test.

c. is always an upper tail test.

d. is always a two-tailed test.

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c

A random sample of 100 high school students was surveyed regarding their favorite subject. The following counts were obtained:

The researcher conducted a test to determine whether the proportion of students was equal for all four subjects. What is the value of the test statistic?

a. 0

b. –4

c. 25

d. 6

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d

If the sample size is n = 75, what are the degrees of freedom for the appropriate chi-square distribution when testing for independence of two variables each with three categories?

a. 74

b. 2

c. 4

d. 69

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b

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.

Freshmen	83
Sophomores	68
Juniors	85
Seniors	64

We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. At a .05 level of significance, the null hypothesis

a. should not be rejected.

b. should be rejected.

c. was designed wrong.

d. cannot be tested.

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a

The number of categorical outcomes per trial for a multinomial probability distribution is

a. three or more.

b. two or more.

c. five or more.

d. four or more.

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a

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

a. 9.348.

b. 7.378.

c. 7.815.

d. 5.991.

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d

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The calculated value for the test statistic equals

a. .01.

b. .75.

c. 4.38.

d. 4.29.

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d

The properties of a multinomial experiment include all of the following except

a. the experiment consists of a sequence of n identical trials.

b. the trials are independent.

c. three or more outcomes are possible on each trial.

d. the probability of each outcome can change from trial to trial.

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d

The properties of a multinomial experiment include all of the following except

a. the experiment consists of a sequence of n identical trials.

b. the trials are independent.

c. three or more outcomes are possible on each trial.

d. the probability of each outcome can change from trial to trial.

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d

The properties of a multinomial experiment include all of the following except

a. the experiment consists of a sequence of n identical trials.

b. the trials are independent.

c. three or more outcomes are possible on each trial.

d. the probability of each outcome can change from trial to trial.

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d

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The expected frequency for the Business College is

a. 105.

b. 90.

c. .3.

d. .35.

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a

How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?

a. 62

b. 74

c. 7

d. 9

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d

You want to test whether or not the following sample of 30 observations follows a normal distribution. The mean of the sample equals 11.83 and the standard deviation equals 4.53.

2	3	5	5	7	8	8	9	9	10
11	11	12	12	12	12	13	13	13	14
15	15	15	16	16	17	17	18	18	19

The number of intervals or categories used to test the hypothesis for this problem is

a. 10.

b. 6.

c. 5.

d. 4.

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b

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The calculated value for the test statistic equals

a. 8.

b. 0.

c. 2.

d. 4.

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a

The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.

Political Party	Support
Democrats	100
Republicans	120
Independents	80

We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The expected frequency for each group is

a. .333.

b. .50.

c. 50.

d. 100.

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d

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The conclusion of the test at the 5% level of significance is that the

a. distribution might have been normal.

b. null hypothesis cannot be rejected.

c. Marascuilo procedure is more applicable.

d. distribution is uniform.

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d

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The p-value is

a. less than .01.

b. between .05 and .1.

c. between .01 and .05.

d. larger than .1.

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d

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The p-value is

a. less than .01.

b. between .05 and .1.

c. between .01 and .05.

d. larger than .1.

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d

When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.

Do you support capital punishment?	Number of individuals
Yes	40
No	60
No Opinion	50

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The p-value is

a. less than .01.

b. between .05 and .1.

c. between .01 and .05.

d. larger than .1.

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d

 A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. The p-value is between

a. .025 to .05.

b. .01 to .025.

c. .05 to .10.

d. .005 to .01.

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a

A Type I error is committed when

a. the critical value is greater than the value of the test statistic.

b. sample data contradict the null hypothesis.

c. a true alternative hypothesis is not accepted.

d. a true null hypothesis is rejected.

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d

When the following hypotheses are being tested at a level of significance of α

H0: μ ≥ 500
Ha: μ < 500

the null hypothesis will be rejected, if the p-value is

a. = α/2.

b. > α.

c. ≤ 1 - α/2.

d. ≤ α.

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d

If the null hypothesis is rejected at the .05 level of significance, it will

a. sometimes not be rejected at the .10 level of significance.

b. always not be rejected at the .10 level of significance.

c. always be rejected at the .10 level of significance.

d. sometimes be rejected at the .10 level of significance.

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c

Read the z statistic from the normal distribution table and circle the correct answer. For a one-tailed test (lower tail) using α = .1020, z =

a. -1.96.

b. -1.27.

c. -1.53.

d. -1.64.

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b

In a one-tailed hypothesis test (lower tail), the test statistic is determined to be -2. The p-value for this test is

a. .0056.

b. .4772.

c. .0228.

d. .5228.

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c

A grocery store has an average sales of $8000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8300 per day. From past information, it is known that the standard deviation of the population is $1200. The correct null hypothesis for this problem is

a. μ = 8000.

b. μ > 8300.

c. μ ≤ 8000.

d. μ ≤ 8300.

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c

Given the following information,

n = 49, x̄ = 50, s = 7
H0: μ ≥ 52
Ha: μ < 52

the test statistic is

a. -2.

b. -1.

c. 1.

d. 2.

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a

For a one-tailed (upper tail) hypothesis test with a sample size of 18 and a .05 level of significance, the critical value of the test statistic t is

a. 1.740.

b. 1.645.

c. 2.110.

d. 1.734.

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a

For a one-tailed hypothesis test (upper tail), the p-value is computed to be .034. If the test is being conducted at the 5% level of significance, the null hypothesis

a. could be rejected or not rejected depending on the sample mean.

b. is rejected.

c. is not rejected.

d. could be rejected or not rejected depending on the sample size.

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b

A school's newspaper reported that the proportion of students majoring in business is at least 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is

a. H0: p ≤ .30    Ha: p > .30.

b. H0: p ≥ .30    Ha: p < .30.

c. H0: p < .30    Ha: p ≥ .30.

d. H0: p > .30    Ha: p ≤ .30.

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b

If the probability of a Type I error (α) is .05, then the probability of a Type II error (β) must be

a. .95.

b. .05.

c. .025.

d. Cannot be computed.

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d

If the sample size increases for a given level of significance, the probability of a Type II error will

a. increase.

b. decrease.

c. remain the same.

d. be equal to 1.0 regardless of α.

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b

The probability of committing a Type I error when the null hypothesis is true as an equality is

a. greater than 1.

b. the level of significance.

c. the confidence level.

d. β.

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b

For the following hypothesis test,

H0: μ ≥ 150
Ha: μ < 150

the test statistic

a. can be either negative or positive.

b. must be positive.

c. must be negative.

d. must be a number between zero and one.

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a

The average manufacturing work week in metropolitan Chattanooga was 40.1 hours last year. It is believed that the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are

a. H0: μ ≥ 40.1     Ha: μ < 40.1.

b. H0: μ < 40.1     Ha: μ ≥ 40.1.

c. H0: μ = 40.1     Ha: μ ≠ 40.1.

d. H0: μ > 40.1     Ha: μ ≤ 40.1.

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a

In hypothesis testing, the critical value is

a. a number that establishes the boundary of the rejection region.

b. the probability of a Type II error.

c. the probability of a Type I error.

d. the same as the p-value.

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a

A weatherman stated that the average temperature during July in Chattanooga is 80 degrees or less. A sample of 32 Julys is taken to test the weatherman's statement. The correct set of hypotheses is

a. H0: μ ≤ 80    Ha: μ > 80.

b. H0: μ < 80    Ha: μ > 80.

c. H0: μ ≠ 80    Ha: μ = 80.

d. H0: μ ≥ 80    Ha: μ < 80.

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a

For a one-tailed hypothesis test (upper tail), the p-value is computed to be .034. If the test is being conducted at the 5% level of significance, the null hypothesis

a. is rejected.

b. could be rejected or not rejected depending on the sample size.

c. could be rejected or not rejected depending on the sample mean.

d. is not rejected.

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a

Read the t statistic from the t distribution table and circle the correct answer. For a one-tailed test (upper tail), using a sample size of 18, and at the 5% level of significance, t =

a. 2.12.

b. -1.740.

c. 1.740.

d. -2.12.

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c

A school's newspaper reported that the proportion of students majoring in business is at least 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is

a. H0: p ≥ .30    Ha: p < .30.

b. H0: p ≤ .30    Ha: p > .30.

c. H0: p < .30    Ha: p ≥ .30.

d. H0: p > .30    Ha: p ≤ .30.

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a

For a two-tailed hypothesis test with a sample size of 20 and a .05 level of significance, the critical values of the test statistic t are

a. -1.729 and 1.729.

b. -2.093 and 2.093.

c. -2.086 and 2.086.

d. -1.725 and 1.725.

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b

The average hourly wage of computer programmers with 2 years of experience has been $21.80. Because of high demand for computer programmers, it is believed there has been a significant increase in the average hourly wage of computer programmers. To test whether or not there has been an increase, the correct hypotheses to be tested are

a. H0: μ < 21.80     Ha: μ ≥ 21.80.

b. H0: μ > 21.80     Ha: μ ≤ 21.80.

c. H0: μ = 21.80     Ha: μ ≠ 21.80.

d. H0: μ ≤ 21.80     Ha: μ > 21.80.

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d

A computer manufacturer claims its computers will perform effectively for more than 5 years. Which pair of hypotheses should be used to test this claim?

a. H0: μ > 5; Ha: μ ≤ 5

b. H0: μ < 5; Ha: μ ≥ 5

c. H0: μ ≤ 5; Ha: μ > 5

d. H0: μ ≥ 5; Ha: μ < 5

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c

If a hypothesis test leads to the rejection of the null hypothesis,

a. a Type I error may have been committed.

b. a Type I error must have been committed.

c. a Type II error may have been committed.

d. a Type II error must have been committed.

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a

When the following hypotheses are being tested at a level of significance of α

H0: μ ≥ 500
Ha: μ < 500

the null hypothesis will be rejected, if the p-value is

a. = α/2.

b. ≤ α.

c. ≤ 1 - α/2.

d. > α.

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b

A grocery store has an average sales of $8000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8300 per day. From past information, it is known that the standard deviation of the population is $1200. The p-value is

a. .9772.

b. .5475.

c. .0228.

d. 2.000.

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c

If the probability of a Type I error (α) is .05, then the probability of a Type II error (β) must be

a. .025.

b. Cannot be computed.

c. .95.

d. .05.

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b

If the null hypothesis is rejected at the .05 level of significance, it will

a. always not be rejected at the .10 level of significance.

b. sometimes not be rejected at the .10 level of significance.

c. sometimes be rejected at the .10 level of significance.

d. always be rejected at the .10 level of significance.

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d

Read the t statistic from the t distribution table and circle the correct answer. For a one-tailed test (upper tail), using a sample size of 18, and at the 5% level of significance, t =

a. 1.740.

b. 2.12.

c. -2.12.

d. -1.740.

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a

The power curve provides the probability of

a. correctly rejecting the null hypothesis.

b. incorrectly rejecting the null hypothesis.

c. correctly accepting the null hypothesis.

d. incorrectly accepting the null hypothesis.

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a

In hypothesis testing, the tentative assumption about the population parameter is

a. the alternative hypothesis.

b. the null hypothesis.

c. either the null or the alternative.

d. neither the null nor the alternative.

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b

A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%. The test statistic is

a. .05.

b. 2.00.

c. 1.25.

d. .80.

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c

For a given sample size in hypothesis testing,

a. the sum of Type I and Type II errors must equal to 1.

b. the smaller the Type I error, the larger the Type II error will be.

c. the smaller the Type I error, the smaller the Type II error will be.

d. Type II error will not be effected by Type I error.

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b

For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic as

a. unlikely as that provided by the sample.

b. likely as that provided by the population.

c. unlikely as that provided by the population.

d. likely as that provided by the sample.

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a

Read the z statistic from the normal distribution table and circle the correct answer. For a one-tailed test (lower tail) using α = .1020, z =

a. -1.27.

b. -1.96.

c. -1.53.

d. -1.64.

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a

Read the z statistic from the normal distribution table and circle the correct answer. For a one-tailed test (upper tail) using α = .1230, z =

a. 1.645.

b. 1.54.

c. 1.16.

d. 1.96.

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c

When the following hypotheses are being tested at a level of significance of α

H0: μ ≥ 500
Ha: μ < 500

the null hypothesis will be rejected, if the p-value is

a. > α.

b. ≤ α.

c. ≤ 1 - α/2.

d. = α/2.

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b

The average monthly rent for one-bedroom apartments in Chattanooga has been $700. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are

a. H0: μ = 700     Ha: μ ≠ 700.

b. H0: μ < 700     Ha: μ ≥ 700.

c. H0: μ ≥ 700     Ha: μ < 700.

d. H0: μ > 700     Ha: μ ≤ 700.

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c

For a lower tail test, the p-value is the probability of obtaining a value for the test statistic

a. at least as large as that provided by the sample.

b. at least as small as that provided by the sample.

c. at least as large as that provided by the population.

d. at least as small as that provided by the population.

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b

The following information was obtained from independent random samples taken of two populations.
Assume normally distributed populations with equal variances.

	Sample 1	Sample 2
Sample Mean	45	42
Sample Variance	85	90
Sample Size	10	12

The 95% confidence interval for the difference between the two population means is (use rounded standard error)

a. -2.65 to 8.65.

b. -4.86 to 10.86.

c. -5.344 to 11.344.

d. -5 to 3.

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c

The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed.

Individual	Method 1	Method 2
1	7	5
2	5	9
3	6	8
4	7	7
5	5	6

The point estimate for the difference between the means of the two populations (Method 1 - Method 2) is

a. 2.

b. 0.

c. -1.

d. -4.

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c

The following information was obtained from matched samples:

If the null hypothesis tested is H0: µd = 0, what is the test statistic for the difference between the two population means?

a. –.48

b. –.50

c. –.24

d. .51

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a

The results of a recent poll on the preference of shoppers regarding two products are shown below.

Product	Shoppers Surveyed	Shoppers Favoring This Product
A	800	560
B	900	612

The 95% confidence interval estimate for the difference between the populations favoring the products is

a. .6 to .7.

b. .046 to .066.

c. -.024 to .064.

d. -.024 to .7.

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c

Salary information regarding male and female employees of a large company is shown below.

	Male	Female
Sample Size	64	36
Sample Mean Salary (in $1000)	44	41
Population Variance (σ2)	128	72

The standard error of the difference between the two sample means is

a. 2.0.

b. 4.

c. 4.24.

d. 7.46.

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a

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

	Today	Five Years Ago
x̄	82	88
σ2	112.5	54
n	45	36

The 95% confidence interval for the difference between the two population means is

a. -3.08 to 3.92.

b. -24.77 to 12.23.

c. -9.92 to -2.08.

d. -13.84 to -1.16.

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c

In a study of whether an exercise routine is effective, the weights of a random sample of individuals before they began the exercise plan and the weights of the same individuals after two months on the exercise plan are recorded. A hypothesis test is conducted to determine if the exercise plan is effective. What is the 95% confidence interval estimate of the mean of the population of differences if n = 30, d̄ = 10.5, and sd = 2.75?

a. The means of the before and after weights must be known to compute the confidence interval.

b. 7.75 to 13.25

c. 9.47 to 11.53

d. 9.65 to 11.35

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c

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the

a. null hypothesis should state p1 - p2 > 0.

b. alternative hypothesis should state p1 - p2 < 0.

c. null hypothesis should state p1 - p2 < 0.

d. alternative hypothesis should state p1 - p2 > 0.

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d

The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information.

	Store's Card	Major Credit Card
Sample size	64	49
Sample mean	$140	$125
Population standard deviation	$10	$8

A 95% confidence interval estimate for the difference between the average purchases of all customers using the two different credit cards is

a. 12.22 to 17.78.

b. 13.04 to 16.96.

c. 13.31 to 16.69.

d. 11.68 to 18.32.

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d

Production output (i.e., number of parts) for a random sample of days from two different plants is shown below.

What is the estimate of the standard deviation for the difference between the two means?

a. 5.12

b. 75

c. 130.34

d. 14.66

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a

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

	Today	Five Years Ago
x̄	82	88
σ2	112.5	54
n	45	36

The standard error of x̄1 - x̄2 is

a. 4.

b. 2.

c. 12.9.

d. 9.3.

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b

The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed.

Individual	Method 1	Method 2
1	7	5
2	5	9
3	6	8
4	7	7
5	5	6

The point estimate for the difference between the means of the two populations (Method 1 - Method 2) is

a. 2.

b. -1.

c. -4.

d. 0.

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b

The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed.

Individual	Method 1	Method 2
1	7	5
2	5	9
3	6	8
4	7	7
5	5	6

The 95% confidence interval for the difference between the two population means is

a. -2.776 to 2.776.

b. -1.776 to 1.776.

c. -3.776 to 1.776.

d. -1.776 to 2.776.

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c

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.

Under Age of 18	Over Age of 18
n1 = 500	n2 = 600
Number of accidents = 180	Number of accidents = 150

We are interested in determining if the accident proportions differ between the two age groups. The pooled estimator of the population proportion is

a. .450.

b. .305.

c. .300.

d. .027.

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c

The following information was obtained from independent random samples taken of two populations.
Assume normally distributed populations with equal variances.

	Sample 1	Sample 2
Sample Mean	45	42
Sample Variance	85	90
Sample Size	10	12

The 95% confidence interval for the difference between the two population means is (use rounded standard error)

a. -5 to 3.

b. -5.344 to 11.344.

c. -2.65 to 8.65.

d. -4.86 to 10.86.

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b

A school administrator is interested in determining whether the proportion of students in the elementary school who are girls (pE) is significantly more than the proportion of students in the high school who are girls (pH). Which set of hypotheses would be most appropriate for answering the administrator's question?

a. H0 : pE – pH = 0     Ha : pE – pH ≠ 0

b. H0 : pE – pH ≤ 0     Ha : pE – pH > 0

c. H0 : pE – pH ≥ 0     Ha : pE – pH < 0

d. H0: pE – pH < 0     Ha: pE – pH ≥ 0

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b

Generally, the ________ sample procedure for inferences about two population means provides better precision than the _______ sample approach.

a. matched, pooled

b. independent, pooled

c. matched, independent

d. single, independent

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c

The following information was obtained from independent random samples taken of two populations.
Assume normally distributed populations with equal variances.

	Sample 1	Sample 2
Sample Mean	45	42
Sample Variance	85	90
Sample Size	10	12

The degrees of freedom for the t distribution are

a. 22.

b. 21.

c. 24.

d. 20.

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d

How many degrees of freedom will the t distribution have when constructing an interval estimate for the difference between the means of two populations if the two population standard deviations are unknown and assumed unequal and the samples sizes of groups 1 and 2 are n1 = 15 and n2 = 18?

a. 33 degrees of freedom

b. 31 degrees of freedom

c. 17 degrees of freedom

d. Not enough information is given to compute the degrees of freedom.

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d

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

	Today	Five Years Ago
x̄	82	88
σ2	112.5	54
n	45	36

The test statistic for the difference between the two population means is

a. -.65.

b. -3.0.

c. -1.5.

d. -.47.

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b

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed.

Driver	Manufacturer A	Manufacturer B
1	32	28
2	27	22
3	26	27
4	26	24
5	25	24
6	29	25
7	31	28
8	25	27

The test statistic is

a. 1.616.

b. 2.096.

c. 1.906.

d. 2.256.

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d

In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered.

	Downtown Store	North Mall Store
Sample size	25	20
Sample mean	$9	$8
Sample standard deviation	$2	$1

A 95% interval estimate for the difference between the two population means is

a. .226 to 1.774.

b. .071 to 1.929.

c. 1.078 to 2.922.

d. 1.09 to 4.078.

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b

The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information.

	Store's Card	Major Credit Card
Sample size	64	49
Sample mean	$140	$125
Population standard deviation	$10	$8

A point estimate for the difference between the mean purchases of all users of the two credit cards is

a. 265.

b. 2.

c. 18.

d. 15.

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d

The results of a recent poll on the preference of shoppers regarding two products are shown below.

Product	Shoppers Surveyed	Shoppers Favoring This Product
A	800	560
B	900	612

The 95% confidence interval estimate for the difference between the populations favoring the products is

a. .6 to .7.

b. -.024 to .064.

c. -.024 to .7.

d. .046 to .066.

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b

The following information was obtained from independent random samples. Suppose we are interested in testing H0: µ1 – µ2 = 15 and Ha: µ1 – µ2 ≠ 15.

What is the test statistic used in the hypothesis test for the difference between the two population means?

a. –5.49

b. .829

c. 14.07

d. –1.37

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a

When each data value in one sample is paired with a corresponding data value in another sample for a sample of 35 individuals or objects and the corresponding differences are computed, what type of distribution will the difference data have?

a. Matched pairs distribution

b. Exponential distribution

c. Uniform distribution

d. t distribution

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d

In testing the null hypothesis H0: μ1 - μ2 = 0, the computed test statistic is z = -1.66. The corresponding p-value is

a. .0970.

b. .9515.

c. .0485.

d. .9030.

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a

The following table shows the predicted sales (in $1000s) and the actual sales (in $1000s) for six stores over a six-month period.

What is the mean of the matched samples data in the above table?

a. 79.5

b. –2.50

c. 80.75

d. 82

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b

The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information.

	Store's Card	Major Credit Card
Sample size	64	49
Sample mean	$140	$125
Population standard deviation	$10	$8

A 95% confidence interval estimate for the difference between the average purchases of all customers using the two different credit cards is

a. 13.04 to 16.96.

b. 12.22 to 17.78.

c. 13.31 to 16.69.

d. 11.68 to 18.32.

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d

How many degrees of freedom will the t distribution have when constructing an interval estimate for the difference between the means of two populations if the two population standard deviations are unknown and assumed unequal and the samples sizes of groups 1 and 2 are n1 = 15 and n2 = 18?

a. 33 degrees of freedom

b. 31 degrees of freedom

c. 17 degrees of freedom

d. Not enough information is given to compute the degrees of freedom.

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d

The following information was obtained from matched samples taken from two populations.
The daily production rates for a sample of workers before and after a training program are shown below. Assume the population of differences is normally distributed.

Worker	Before	After
1	20	22
2	25	23
3	27	27
4	23	20
5	22	25
6	20	19
7	17	18

The point estimate for the difference between the means of the two populations is

a. -2.

b. -1.

c. 0.

d. 1.

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c

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.

Under Age of 18	Over Age of 18
n1 = 500	n2 = 600
Number of accidents = 180	Number of accidents = 150

We are interested in determining if the accident proportions differ between the two age groups. The p-value is

a. .3.

b. less than .001.

c. .0228.

d. more than .10.

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b

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Salary information regarding male and female employees of a large company is shown below.

	Male	Female
Sample Size	64	36
Sample Mean Salary (in $1000)	44	41
Population Variance (σ2)	128	72

At 95% confidence, the margin of error is

a. 1.960.

b. 3.920.

c. 2.000.

d. 1.645.

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b

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed.

Driver	Manufacturer A	Manufacturer B
1	32	28
2	27	22
3	26	27
4	26	24
5	25	24
6	29	25
7	31	28
8	25	27

The mean of the differences is

a. 2.0.

b. 2.5.

c. .5.

d. 1.5.

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a

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as

a. independent samples.

b. matched samples.

c. pooled samples.

d. corresponding samples.

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b

Two independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the

a. t distribution with 60 degrees of freedom.

b. t distribution with 58 degrees of freedom.

c. t distribution with 61 degrees of freedom.

d. t distribution with 59 degrees of freedom.

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b

The following information was obtained from matched samples taken from two populations.
The daily production rates for a sample of workers before and after a training program are shown below. Assume the population of differences is normally distributed.

Worker	Before	After
1	20	22
2	25	23
3	27	27
4	23	20
5	22	25
6	20	19
7	17	18

The null hypothesis to be tested is H0: μd = 0. The test statistic is

a. 0.

b. -1.96.

c. 1.00.

d. 1.77.

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a

Random samples of 100 parts from production line A had 12 parts that were defective and 100 parts from production line B had 5 that were defective. What is the test statistic for the hypothesis test of a difference between the two proportions?

a. z = 1.96

b. z = 2.16

c. z = .07

d. z = 1.77

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d

In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of Rock City recently undertook an extensive promotional campaign. They are interested in determining whether the promotional campaign actually increased the proportion of tourists visiting Rock City. The correct set of hypotheses is

a. H0: p > .75    Ha: p ≤  .75.

b. H0: p ≤  .75    Ha: p > .75.

c. H0: p < .75    Ha: p ≥  .75.

d. H0: p ≥  .75      Ha: p < .75.

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b

Batteries produced by a manufacturing company have had a life expectancy of 135 hours. Because of an improved production process, the company believes that there has been an increase in the life expectancy of its batteries. A sample of 42 batteries showed an average life of 140 hours. From past information, the standard deviation of the population is known to be 24 hours. Test to determine whether there has been an increase in the life expectancy of batteries. What is the test statistic, and what conclusion can be made at the .10 level of significance?

a. z = 2.33; Reject the null hypothesis

b. z = 1.35; Reject the null hypothesis

c. z = .088; Do not reject the null hypothesis

d. z = .208; Do not reject the null hypothesis

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b

Read the t statistic from the t distribution table and circle the correct answer. For a one-tailed test (upper tail), using a sample size of 18, and at the 5% level of significance, t =

a. 1.740.

b. -2.12.

c. 2.12.

d. -1.740.

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a

The p-value is a probability that measures the support (or lack of support) for

a. the null hypothesis.

b. either the null or the alternative hypothesis.

c. neither the null nor the alternative hypothesis.

d. the alternative hypothesis.

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a

A weatherman stated that the average temperature during July in Chattanooga is 80 degrees or less. A sample of 32 Julys is taken to test the weatherman's statement. The correct set of hypotheses is

a. H0: μ ≤ 80    Ha: μ > 80.

b. H0: μ ≠ 80    Ha: μ = 80.

c. H0: μ ≥ 80    Ha: μ < 80.

d. H0: μ < 80    Ha: μ > 80.

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a

The average monthly rent for one-bedroom apartments in Chattanooga has been $700. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are

a. H0: μ > 700     Ha: μ ≤ 700.

b. H0: μ < 700     Ha: μ ≥ 700.

c. H0: μ = 700     Ha: μ ≠ 700.

d. H0: μ ≥ 700     Ha: μ < 700.

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d

For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test,

a. Not enough information is given to answer this question.

b. will result in the area corresponding to the critical value being larger.

c. will result in the area corresponding to the critical value being smaller.

d. will have no effect on the area corresponding to the critical value.

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c

Read the t statistic from the t distribution table and circle the correct answer. For a one-tailed test (lower tail), using a sample size of 10, and at the 10% level of significance, t =

a. -1.383.

b. -2.821.

c. 1.383.

d. 2.821.

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a

For a one-tailed hypothesis test (upper tail), the p-value is computed to be .034. If the test is being conducted at the 5% level of significance, the null hypothesis

a. is not rejected.

b. could be rejected or not rejected depending on the sample size.

c. could be rejected or not rejected depending on the sample mean.

d. is rejected.

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d

If the cost of making a Type I error is high, a smaller value should be chosen for the

a. confidence coefficient.

b. level of significance.

c. critical value.

d. test statistic.

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b

Read the z statistic from the normal distribution table and circle the correct answer. For a one-tailed test (upper tail) at α = .0630, z =

a. 1.645.

b. 1.50.

c. 1.53.

d. 1.96.

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c

For a one-tailed hypothesis test (upper tail), the p-value is computed to be .034. If the test is being conducted at the 5% level of significance, the null hypothesis

a. is rejected.

b. could be rejected or not rejected depending on the sample size.

c. could be rejected or not rejected depending on the sample mean.

d. is not rejected.

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a

A school's newspaper reported that the proportion of students majoring in business is at least 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is

a. H0: p ≤ .30    Ha: p > .30.

b. H0: p > .30    Ha: p ≤ .30.

c. H0: p < .30    Ha: p ≥ .30.

d. H0: p ≥ .30    Ha: p < .30.

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d

If the cost of making a Type I error is high, a smaller value should be chosen for the

a. confidence coefficient.

b. level of significance.

c. test statistic.

d. critical value.

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b

The average hourly wage of computer programmers with 2 years of experience has been $21.80. Because of high demand for computer programmers, it is believed there has been a significant increase in the average hourly wage of computer programmers. To test whether or not there has been an increase, the correct hypotheses to be tested are

a. H0: μ < 21.80     Ha: μ ≥ 21.80.

b. H0: μ > 21.80     Ha: μ ≤ 21.80.

c. H0: μ ≤ 21.80     Ha: μ > 21.80.

d. H0: μ = 21.80     Ha: μ ≠ 21.80.

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c

Your investment executive claims that the average yearly rate of return on the stocks she recommends is at least 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is

a. H0: μ < 10.0%    Ha: μ ≥ 10.0%.

b. H0: μ ≥ 10.0%    Ha: μ < 10.0%.

c. H0: μ > 10.0%    Ha: μ ≤ 10.0%.

d. H0: μ ≤ 10.0%    Ha: μ > 10.0%.

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b

The sum of the values of α and β

a. is always 1.

b. is always .5.

c. gives the probability of taking the correct decision.

d. is not needed in hypothesis testing.

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d

For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic as

a. unlikely as that provided by the population.

b. unlikely as that provided by the sample.

c. likely as that provided by the population.

d. likely as that provided by the sample.

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b

A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. Using α = .05, it can be concluded that the population mean age is

a. not significantly different from 24.

b. significantly more than 24.

c. significantly less than 24.

d. significantly different from 24.

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b

If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error

a. will decrease.

b. will also increase from .01 to .05.

c. will not change.

d. will increase.

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a

The average monthly rent for one-bedroom apartments in Chattanooga has been $700. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are

a. H0: μ ≥ 700     Ha: μ < 700.

b. H0: μ = 700     Ha: μ ≠ 700.

c. H0: μ < 700     Ha: μ ≥ 700.

d. H0: μ > 700     Ha: μ ≤ 700.

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a

A computer manufacturer claims its computers will perform effectively for more than 5 years. Which pair of hypotheses should be used to test this claim?

a. H0: μ > 5; Ha: μ ≤ 5

b. H0: μ < 5; Ha: μ ≥ 5

c. H0: μ ≥ 5; Ha: μ < 5

d. H0: μ ≤ 5; Ha: μ > 5

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d

The probability of making a Type I error is denoted by

a. β.

b. α.

c. 1 - β.

d. 1 - α.

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b

A grocery store has an average sales of $8000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8300 per day. From past information, it is known that the standard deviation of the population is $1200. The value of the test statistic is

a. 2.00.

b. 80.00.

c. .25.

d. 8.25.

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a

A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%. The p-value is

a. .2112.

b. .025.

c. .05.

d. .1056.

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d

A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. Using α = .05, it can be concluded that the population mean age is

a. significantly less than 24.

b. significantly different from 24.

c. significantly more than 24.

d. not significantly different from 24.

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c

If the cost of making a Type I error is high, a smaller value should be chosen for the

a. confidence coefficient.

b. level of significance.

c. critical value.

d. test statistic.

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b

An assumption made about the value of a population parameter is called a(n)

a. error.

b. conclusion.

c. hypothesis.

d. probability.

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c

Read the z statistic from the normal distribution table and circle the correct answer. For a two-tailed test using α = .0160, z =

a. 2.41.

b. 1.96.

c. 1.14.

d. .86.

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a

The critical value of t for a two-tailed test with 6 degrees of freedom using α = .05 is

a. 1.985.

b. 2.365.

c. 2.447.

d. 1.943.

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c

Which of the following approaches cannot be used to perform a two-tailed hypothesis test about μ?

a. Compare the p-value to the value of α.

b. Compare the confidence interval estimate of μ to the hypothesized value of μ.

c. Compare the level of significance to the confidence coefficient.

d. Compare the value of the test statistic to the critical value.

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c

When the null hypothesis is rejected, it is

a. not possible a Type I error has occurred.

b. possible either a Type I or a Type II error has occurred.

c. possible a Type II error has occurred.

d. possible a Type I error has occurred.

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d

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

a. α < p-value.

b. p-value = x̄.

c. p-value < ζ.

d. p-value ≤ α.

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d

The manager of a laptop computer dealership is considering a new bonus plan in order to increase sales. Currently, the mean sales rate per salesperson is five laptops per week. The correct set of hypotheses for testing the effect of the bonus plan is

a. H0: μ < 5    Ha: μ ≥ 5.

b. H0: μ ≥ 5    Ha: μ < 5.

c. H0: μ > 5    Ha: μ ≤ 5.

d. H0: μ ≤ 5    Ha: μ > 5.

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d

In hypothesis tests about a population proportion, p0 represents the

a. observed sample proportion.

b. observed p-value.

c. probability that H0 is correct.

d. hypothesized population proportion.

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d

If the null hypothesis is rejected at the 5% level of significance, it

a. will always be rejected at the 1% level.

b. will never be tested at the 1% level.

c. will always not be rejected at the 1% level.

d. may be rejected or not rejected at the 1% level.

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d

For a two-tailed hypothesis test with a sample size of 20 and a .05 level of significance, the critical values of the test statistic t are

a. -1.725 and 1.725.

b. -2.093 and 2.093.

c. -1.729 and 1.729.

d. -2.086 and 2.086.

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b

In a lower tail hypothesis test situation, the p-value is determined to be .2. If the sample size for this test is 51, the t statistic has a value of

a. -.849.

b. -1.299.

c. .849.

d. 1.299.

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a

For a two-tailed hypothesis test about μ, we can use any of the following approaches except

a. compare the p-value to the value of α.

b. compare the value of the test statistic to the critical value.

c. compare the level of significance to the confidence coefficient.

d. compare the confidence interval estimate of μ to the hypothesized value of μ.

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c

Read the t statistic from the t distribution table and circle the correct answer. For a one-tailed test (lower tail), using a sample size of 10, and at the 10% level of significance, t =

a. -2.821.

b. 2.821.

c. -1.383.

d. 1.383.

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c

The average monthly rent for one-bedroom apartments in Chattanooga has been $700. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are

a. H0: μ = 700     Ha: μ ≠ 700.

b. H0: μ < 700     Ha: μ ≥ 700.

c. H0: μ > 700     Ha: μ ≤ 700.

d. H0: μ ≥ 700     Ha: μ < 700.

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d

In a one-tailed hypothesis test (lower tail), the test statistic is determined to be -2. The p-value for this test is

a. .4772.

b. .0228.

c. .0056.

d. .5228.

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b

A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. The p-value is between

a. .025 to .05.

b. .01 to .025.

c. .05 to .10.

d. .005 to .01.

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a 

Read the z statistic from the normal distribution table and circle the correct answer. For a two-tailed test using α = .1388, z =

a. .86.

b. 1.09.

c. 1.96.

d. 1.48.

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d

When the null hypothesis is rejected, it is

a. possible a Type II error has occurred.

b. possible a Type I error has occurred.

c. possible either a Type I or a Type II error has occurred.

d. not possible a Type I error has occurred.

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b

Read the t statistic from the t distribution table and circle the correct answer. For a one-tailed test (lower tail), using a sample size of 10, and at the 10% level of significance, t =

a. 1.383.

b. 2.821.

c. -2.821.

d. -1.383.

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d

Given the following information,

n = 49, x̄ = 50, s = 7
H0: μ ≥ 52
Ha: μ < 52

the test statistic is

a. 1.

b. -2.

c. 2.

d. -1.

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b

Batteries produced by a manufacturing company have had a life expectancy of 135 hours. Because of an improved production process, the company believes that there has been an increase in the life expectancy of its batteries. A sample of 42 batteries showed an average life of 140 hours. From past information, the standard deviation of the population is known to be 24 hours. Test to determine whether there has been an increase in the life expectancy of batteries. What is the test statistic, and what conclusion can be made at the .10 level of significance?

a. z = 2.33; Reject the null hypothesis

b. z = .208; Do not reject the null hypothesis

c. z = .088; Do not reject the null hypothesis

d. z = 1.35; Reject the null hypothesis

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d

The p-value is

a. a probability.

b. the same as the z statistic.

c. a distance.

d. a sample statistic.

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a

In hypothesis testing, the critical value is

a. the same as the p-value.

b. the probability of a Type I error.

c. the probability of a Type II error.

d. a number that establishes the boundary of the rejection region.

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d

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

	Today	Five Years Ago
x̄	82	88
σ2	112.5	54
n	45	36

What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? (Use a .05 level of significance.)

a. There is no statistically significant difference in the average final examination scores between the two classes.

b. The students who enrolled in statistics today are the same students who enrolled five years ago.

c. It is impossible to make a decision on the basis of the information given.

d. There is a statistically significant difference in the average final examination scores between the two classes.

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d

The results of a recent poll on the preference of shoppers regarding two products are shown below.

Product	Shoppers Surveyed	Shoppers Favoring This Product
A	800	560
B	900	612

The point estimate for the difference between the two population proportions in favor of this product is

a. .68.

b. .02.

c. .44.

d. .07.

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b

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.

Under Age of 18	Over Age of 18
n1 = 500	n2 = 600
Number of accidents = 180	Number of accidents = 150

We are interested in determining if the accident proportions differ between the two age groups. The pooled estimator of the population proportion is

a. .300.

b. .027.

c. .450.

d. .305.

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a

The following information was obtained from matched samples taken from two populations.
The daily production rates for a sample of workers before and after a training program are shown below. Assume the population of differences is normally distributed.

Worker	Before	After
1	20	22
2	25	23
3	27	27
4	23	20
5	22	25
6	20	19
7	17	18

The point estimate for the difference between the means of the two populations is

a. 1.

b. 0.

c. -2.

d. -1.

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b

The following information was obtained from independent random samples taken of two populations.
Assume normally distributed populations with equal variances.

	Sample 1	Sample 2
Sample Mean	45	42
Sample Variance	85	90
Sample Size	10	12

The degrees of freedom for the t distribution are

a. 20.

b. 24.

c. 21.

d. 22.

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a

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed.

Driver	Manufacturer A	Manufacturer B
1	32	28
2	27	22
3	26	27
4	26	24
5	25	24
6	29	25
7	31	28
8	25	27

At α = .10, the null hypothesis

a. should not be tested.

b. should not be rejected.

c. should be revised.

d. should be rejected.

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d

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

	Today	Five Years Ago
x̄	82	88
σ2	112.5	54
n	45	36

The test statistic for the difference between the two population means is

a. -.47.

b. -.65.

c. -3.0.

d. -1.5.

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c

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.

Under Age of 18	Over Age of 18
n1 = 500	n2 = 600
Number of accidents = 180	Number of accidents = 150

We are interested in determining if the accident proportions differ between the two age groups. The p-value is

a. .3.

b. .0228.

c. more than .10.

d. less than .001.

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d

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

	Today	Five Years Ago
x̄	82	88
σ2	112.5	54
n	45	36

The p-value for the difference between the two population means is

a. .0026.

b. .4987.

c. .0013.

d. .9987.

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a

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

	Today	Five Years Ago
x̄	82	88
σ2	112.5	54
n	45	36

The 95% confidence interval for the difference between the two population means is

a. -13.84 to -1.16.

b. -3.08 to 3.92.

c. -24.77 to 12.23.

d. -9.92 to -2.08.

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d

The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed.

Individual	Method 1	Method 2
1	7	5
2	5	9
3	6	8
4	7	7
5	5	6

The 95% confidence interval for the difference between the two population means is

a. -1.776 to 2.776.

b. -2.776 to 2.776.

c. -1.776 to 1.776.

d. -3.776 to 1.776.

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d

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

	Today	Five Years Ago
x̄	82	88
σ2	112.5	54
n	45	36

The point estimate for the difference between the means of the two populations is

a. -6.

b. 9.

c. -9.

d. 58.5.

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a

Generally, the ________ sample procedure for inferences about two population means provides better precision than the _______ sample approach.

a. single, independent

b. matched, pooled

c. matched, independent

d. independent, pooled

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c

The results of a recent poll on the preference of shoppers regarding two products are shown below.

Product	Shoppers Surveyed	Shoppers Favoring This Product
A	800	560
B	900	612

The point estimate for the difference between the two population proportions in favor of this product is

a. .02.

b. .07.

c. .68.

d. .44.

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a

The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information.

	Store's Card	Major Credit Card
Sample size	64	49
Sample mean	$140	$125
Population standard deviation	$10	$8

At 95% confidence, the margin of error is

a. 3.32.

b. 1.96.

c. 15.

d. 1.694.

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a

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as

a. corresponding samples.

b. pooled samples.

c. independent samples.

d. matched samples.

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d

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the

a. null hypothesis should state p1 - p2 > 0.

b. alternative hypothesis should state p1 - p2 > 0.

c. alternative hypothesis should state p1 - p2 < 0.

d. null hypothesis should state p1 - p2 < 0.

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b

The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information.

	Store's Card	Major Credit Card
Sample size	64	49
Sample mean	$140	$125
Population standard deviation	$10	$8

A point estimate for the difference between the mean purchases of all users of the two credit cards is

a. 2.

b. 265.

c. 15.

d. 18.

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c

The results of a recent poll on the preference of shoppers regarding two products are shown below.

Product	Shoppers Surveyed	Shoppers Favoring This Product
A	800	560
B	900	612

At 95% confidence, the margin of error is

a. .064.

b. .044.

c. .025.

d. .0225.

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b

In hypothesis tests about p1 - p2, the pooled estimator of p is a(n)

a. weighted average of p̄1 and p̄2.

b. geometric average of p̄1 and p̄2.

c. simple average of p̄1 and p̄2.

d. exponential average of p̄1 and p̄2.

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a

The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information.

	Store's Card	Major Credit Card
Sample size	64	49
Sample mean	$140	$125
Population standard deviation	$10	$8

A point estimate for the difference between the mean purchases of all users of the two credit cards is

a. 18.

b. 15.

c. 2.

d. 265.

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b

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as

a. independent samples.

b. matched samples.

c. pooled samples.

d. corresponding samples.

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b

A researcher is interested in determining whether the mean of group 1 is 10 units larger than the mean of group 2. Which of the following represents the alternative hypothesis for testing the researcher's theory?

a. Ha: µ1 – µ2 > 10

b. Ha: µ 1 – µ2 ≤ 10

c. Ha: µ1 = µ2

d. Ha:µ1 – µ2 = 0

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a

The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.

Music Type	Teenagers Surveyed	Teenagers Favoring This Type
Pop	800	384
Rap	900	450

The point estimate of the difference between the two population proportions is

a. .048.

b. -.5.

c. -.02.

d. .52.

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c

Regarding inferences about the difference between two population means, the sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on

a. research samples.

b. conditional samples.

c. pooled samples.

d. independent samples.

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d

The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed.

Individual	Method 1	Method 2
1	7	5
2	5	9
3	6	8
4	7	7
5	5	6

The 95% confidence interval for the difference between the two population means is

a. -1.776 to 2.776.

b. -2.776 to 2.776.

c. -3.776 to 1.776.

d. -1.776 to 1.776.

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c

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.

Under Age of 18	Over Age of 18
n1 = 500	n2 = 600
Number of accidents = 180	Number of accidents = 150

We are interested in determining if the accident proportions differ between the two age groups. The pooled estimator of the population proportion is

a. .305.

b. .300.

c. .450.

d. .027.

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b

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.

Under Age of 18	Over Age of 18
n1 = 500	n2 = 600
Number of accidents = 180	Number of accidents = 150

We are interested in determining if the accident proportions differ between the two age groups. The p-value is

a. less than .001.

b. .3.

c. more than .10.

d. .0228.

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a

The local cable company is interested in determining whether or not the proportion of subscribers has increased during the past year. A random sample of households selected last year is compared with a random sample of households selected this year. Results are summarized below.

What is the value of the pooled estimate of p?

a. .708

b. .657

c. .085

d. .23

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a

Of the two production methods, a company wants to identify the method with the smaller population mean completion time. One sample of workers is selected and each worker first uses one method and then uses the other method. The sampling procedure being used to collect completion time data is based on

a. independent samples.

b. matched samples.

c. pooled samples.

d. worker samples.

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b

The results of a recent poll on the preference of shoppers regarding two products are shown below.

Product	Shoppers Surveyed	Shoppers Favoring This Product
A	800	560
B	900	612

The point estimate for the difference between the two population proportions in favor of this product is

a. .68.

b. .44.

c. .07.

d. .02.

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d

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated.

	Company A	Company B
Sample size	80	60
Sample mean	$16.75	$16.25
Population standard deviation	$1.00	$.95

The test statistic is

a. 3.01.

b. 2.75.

c. 1.645.

d. .098.

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a

In hypothesis tests about p1 - p2, the pooled estimator of p is a(n)

a. exponential average of p̄1 and p̄2.

b. weighted average of p̄1 and p̄2.

c. simple average of p̄1 and p̄2.

d. geometric average of p̄1 and p̄2.

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b

The local cable company is interested in determining whether or not the proportion of subscribers has increased during the past year. A random sample of households selected last year is compared with a random sample of households selected this year. Results are summarized below.

What is the value of the pooled estimate of p?

a. .657

b. .708

c. .23

d. .085

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b

Salary information regarding male and female employees of a large company is shown below.

	Male	Female
Sample Size	64	36
Sample Mean Salary (in $1000)	44	41
Population Variance (σ2)	128	72

If you are interested in testing whether or not the population average salary of males is significantly greater than that of females, the test statistic is

a. 2.0.

b. 1.645.

c. 1.5.

d. 1.96.

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c

A school administrator is interested in determining whether the proportion of students in the elementary school who are girls (pE) is significantly more than the proportion of students in the high school who are girls (pH). Which set of hypotheses would be most appropriate for answering the administrator's question?

a. H0: pE – pH < 0     Ha: pE – pH ≥ 0

b. H0 : pE – pH ≥ 0     Ha : pE – pH < 0

c. H0 : pE – pH = 0     Ha : pE – pH ≠ 0

d. H0 : pE – pH ≤ 0     Ha : pE – pH > 0

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d

The results of a recent poll on the preference of shoppers regarding two products are shown below.

Product	Shoppers Surveyed	Shoppers Favoring This Product
A	800	560
B	900	612

The standard error of p̄1 - p̄2 is

a. .025.

b. .0225.

c. .68.

d. .044.

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b

To compute an interval estimate for the difference between the means of two populations, the t distribution

a. is not restricted to small sample situations.

b. can be applied when the populations have equal means.

c. can be applied only when the populations have equal standard deviations.

d. is restricted to small sample situations.

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a

The sampling distribution of p̄1 - p̄2 is approximated by a

a. t distribution with n1 + n2 - 1 degrees of freedom.

b. p̄1 - p̄2 distribution.

c. normal distribution.

d. t distribution with n1 + n2 degrees of freedom.

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c

The standard error of x̄1 - x̄2 is the

a. variance of the sampling distribution of x̄1 - x̄2.

b. standard deviation of the sampling distribution of x̄1 - x̄2.

c. margin of error of x̄1 - x̄2.

d. pooled estimator of x̄1 - x̄2.

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b

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as

a. independent samples.

b. pooled samples.

c. matched samples.

d. corresponding samples.

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c

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have equal variances, we must use a t distribution with (let n1 be the size of sample 1 and n2 the size of sample 2)

a. (n1 + n2 - 1) degrees of freedom.

b. (n1 - n2 + 2) degrees of freedom.

c. (n1 + n2) degrees of freedom.

d. (n1 + n2 - 2) degrees of freedom.

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d

In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered.

	Downtown Store	North Mall Store
Sample size	25	20
Sample mean	$9	$8
Sample standard deviation	$2	$1

A 95% interval estimate for the difference between the two population means is

a. .226 to 1.774.

b. .071 to 1.929.

c. 1.09 to 4.078.

d. 1.078 to 2.922.

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b

Two independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the

a. t distribution with 60 degrees of freedom.

b. t distribution with 61 degrees of freedom.

c. t distribution with 58 degrees of freedom.

d. t distribution with 59 degrees of freedom.

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c

In hypothesis tests about p1 - p2, the pooled estimator of p is a(n)

a. simple average of p̄1 and p̄2.

b. weighted average of p̄1 and p̄2.

c. exponential average of p̄1 and p̄2.

d. geometric average of p̄1 and p̄2.

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b

The following information was obtained from independent random samples taken of two populations.
Assume normally distributed populations with equal variances.

	Sample 1	Sample 2
Sample Mean	45	42
Sample Variance	85	90
Sample Size	10	12

The point estimate for the difference between the means of the two populations is

a. 2.

b. 15.

c. 3.

d. 0.

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c

Salary information regarding male and female employees of a large company is shown below.

	Male	Female
Sample Size	64	36
Sample Mean Salary (in $1000)	44	41
Population Variance (σ2)	128	72

The 95% confidence interval for the difference between the means of the two populations is

a. -2 to 2.

b. 0 to 6.92.

c. -1.96 to 1.96.

d. -.92 to 6.92.

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d

The following information was obtained from independent random samples taken of two populations.
Assume normally distributed populations with equal variances.

	Sample 1	Sample 2
Sample Mean	45	42
Sample Variance	85	90
Sample Size	10	12

The degrees of freedom for the t distribution are

a. 22.

b. 21.

c. 24.

d. 20.

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d

The following information was obtained from independent random samples taken of two populations.
Assume normally distributed populations with equal variances.

	Sample 1	Sample 2
Sample Mean	45	42
Sample Variance	85	90
Sample Size	10	12

The 95% confidence interval for the difference between the two population means is (use rounded standard error)

a. -2.65 to 8.65.

b. -4.86 to 10.86.

c. -5.344 to 11.344.

d. -5 to 3.

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c

In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered.

	Downtown Store	North Mall Store
Sample size	25	20
Sample mean	$9	$8
Sample standard deviation	$2	$1

A point estimate for the difference between the two population means is

a. 2.

b. 1.

c. 3.

d. 4.

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b

A sample of 1400 items had 280 defective items. For the following hypothesis test,

H0: p ≤ .20
Ha: p > .20

the test statistic is

a. .20.

b. .28.

c. .14.

d. zero.

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d

Read the t statistic from the t distribution table and circle the correct answer. For a one-tailed test (upper tail) with a sample size of 26 and at the .10 level, t =

a. -1.316.

b. 1.740.

c. -1.740.

d. 1.316.

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d

A school's newspaper reported that the proportion of students majoring in business is at least 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is

a. H0: p ≤ .30    Ha: p > .30.

b. H0: p > .30    Ha: p ≤ .30.

c. H0: p ≥ .30    Ha: p < .30.

d. H0: p < .30    Ha: p ≥ .30.

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c

Which of the following does not need to be known in order to compute the p-value?

a. the probability distribution of the test statistic

b. knowledge of whether the test is one-tailed or two-tailed

c. the level of significance

d. the value of the test statistic

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c

A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is

a. H0: μ ≥ 85     Ha: μ < 85.

b. H0: μ < 85     Ha: μ ≥ 85.

c. H0: μ ≤ 85     Ha: μ > 85.

d. H0: μ > 85     Ha: μ ≤ 85.

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a

Read the t statistic from the t distribution table and circle the correct answer. For a two-tailed test with a sample size of 20 and using α = .20, t =

a. 2.539.

b. 1.325.

c. 1.328.

d. 2.528.

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c

A weatherman stated that the average temperature during July in Chattanooga is 80 degrees or less. A sample of 32 Julys is taken to test the weatherman's statement. The correct set of hypotheses is

a. H0: μ < 80    Ha: μ > 80.

b. H0: μ ≥ 80    Ha: μ < 80.

c. H0: μ ≠ 80    Ha: μ = 80.

d. H0: μ ≤ 80    Ha: μ > 80.

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d

The p-value is a probability that measures the support (or lack of support) for

a. the alternative hypothesis.

b. the null hypothesis.

c. either the null or the alternative hypothesis.

d. neither the null nor the alternative hypothesis.

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b

Read the z statistic from the normal distribution table and circle the correct answer. For a one-tailed test (upper tail) at α = .0630, z =

a. 1.96.

b. 1.50.

c. 1.53.

d. 1.645.

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c

Read the z statistic from the normal distribution table and circle the correct answer. For a one-tailed test (upper tail) at α = .0630, z =

a. 1.96.

b. 1.50.

c. 1.53.

d. 1.645.

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c

Generally, the ________ sample procedure for inferences about two population means provides better precision than the _______ sample approach.

a. matched, independent

b. single, independent

c. independent, pooled

d. matched, pooled

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a

The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.

Music Type	Teenagers Surveyed	Teenagers Favoring This Type
Pop	800	384
Rap	900	450

The 95% confidence interval for the difference between the two population proportions is

a. .48 to .5.

b. .028 to .068.

c. .5 to .52.

d. -.068 to .028.

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d

The following information was obtained from matched samples taken from two populations.
The daily production rates for a sample of workers before and after a training program are shown below. Assume the population of differences is normally distributed.

Worker	Before	After
1	20	22
2	25	23
3	27	27
4	23	20
5	22	25
6	20	19
7	17	18

The null hypothesis to be tested is H0: μd = 0. The test statistic is

a. -1.96.

b. 1.00.

c. 0.

d. 1.77.

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c

Production output (i.e., number of parts) for a random sample of days from two different plants is shown below.

What is the estimate of the standard deviation for the difference between the two means?

a. 14.66

b. 5.12

c. 75

d. 130.34

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b

In testing the null hypothesis H0: μ1 - μ2 = 0, the computed test statistic is z = -1.66. The corresponding p-value is

a. .0485.

b. .9030.

c. .0970.

d. .9515.

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c

Two independent simple random samples are taken to test the difference between the means of two populations whose variances are not known, but are assumed to be equal. The sample sizes are n1 = 32 and n2 = 40. The correct distribution to use is the

a. t distribution with 72 degrees of freedom.

b. t distribution with 71 degrees of freedom.

c. t distribution with 73 degrees of freedom.

d. t distribution with 70 degrees of freedom.

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d

The following information was obtained from independent random samples. Suppose we are interested in testing H0: µ1 – µ2 = 15 and Ha: µ1 – µ2 ≠ 15.

What is the test statistic used in the hypothesis test for the difference between the two population means?

a. –1.37

b. 14.07

c. .829

d. –5.49

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d

• Check My Work

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

	Today	Five Years Ago
x̄	82	88
σ2	112.5	54
n	45	36

The standard error of x̄1 - x̄2 is

a. 2.

b. 12.9.

c. 4.

d. 9.3.

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a

When each data value in one sample is paired with a corresponding data value in another sample for a sample of 35 individuals or objects and the corresponding differences are computed, what type of distribution will the difference data have?

a. t distribution

b. Matched pairs distribution

c. Uniform distribution

d. Exponential distribution

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a

The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed.

Individual	Method 1	Method 2
1	7	5
2	5	9
3	6	8
4	7	7
5	5	6

The 95% confidence interval for the difference between the two population means is

a. -3.776 to 1.776.

b. -1.776 to 1.776.

c. -2.776 to 2.776.

d. -1.776 to 2.776.

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a

Two approaches to drawing a conclusion in a hypothesis test are

a. p-value and critical value.

b. one-tailed and two-tailed.

c. Type I and Type II.

d. null and alternative.

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a

A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. The test statistic is

a. .05.

b. 1.96.

c. 2.00.

d. 1.65.

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c

For a given sample size in hypothesis testing,

a. the smaller the Type I error, the larger the Type II error will be.

b. the sum of Type I and Type II errors must equal to 1.

c. the smaller the Type I error, the smaller the Type II error will be.

d. Type II error will not be effected by Type I error.

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a

In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of Rock City recently undertook an extensive promotional campaign. They are interested in determining whether the promotional campaign actually increased the proportion of tourists visiting Rock City. The correct set of hypotheses is

a. H0: p > .75    Ha: p ≤  .75.

b. H0: p < .75    Ha: p ≥  .75.

c. H0: p ≤  .75    Ha: p > .75.

d. H0: p ≥  .75      Ha: p < .75.

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c

If the sample size increases for a given level of significance, the probability of a Type II error will

a. increase.

b. decrease.

c. remain the same.

d. be equal to 1.0 regardless of α.

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b

For a two-tailed hypothesis test with a sample size of 20 and a .05 level of significance, the critical values of the test statistic t are

a. -2.086 and 2.086.

b. -1.729 and 1.729.

c. -2.093 and 2.093.

d. -1.725 and 1.725.

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c

Which of the following statements is true with respect to hypothesis testing?

a. All hypothesis tests are two-sided.

b. The p-value approach and critical value approach will always provide the same hypothesis-testing conclusion.

c. The level of significance must be known before computing a p-value for a hypothesis test.

d. All of these choices are true.

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b

For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test,

a. will have no effect on the area corresponding to the critical value.

b. will result in the area corresponding to the critical value being smaller.

c. Not enough information is given to answer this question.

d. will result in the area corresponding to the critical value being larger.

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b

For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test,

a. will have no effect on the area corresponding to the critical value.

b. will result in the area corresponding to the critical value being smaller.

c. Not enough information is given to answer this question.

d. will result in the area corresponding to the critical value being larger.

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b

For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test,

a. will have no effect on the area corresponding to the critical value.

b. will result in the area corresponding to the critical value being smaller.

c. Not enough information is given to answer this question.

d. will result in the area corresponding to the critical value being larger.

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b

Which of the following represents a Type I error for the null and alternative hypotheses H0: μ ≤ $3,200 and Ha: μ > $3,200, where μ is the average amount of money in a savings account for a person aged 30 to 40?

a. A Type I error would occur if we reject H0 and conclude that the average age is less than 30 when in fact the average age is greater than 40.

b. A Type I error would occur if we reject H0 and conclude that the average amount is greater than $3,200 when in fact the average amount is $3,200 or less.

c. A Type I error would occur if we fail to reject H0 and conclude that the average amount is $3,200 or less when in fact the average amount is greater than $3,200.

d. A Type I error would occur if we fail to reject H0 and conclude that the average amount is less than or equal to $3,200 when in fact the average amount is $3,200 or less.

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b

The p-value is a probability that measures the support (or lack of support) for

a. the alternative hypothesis.

b. the null hypothesis.

c. either the null or the alternative hypothesis.

d. neither the null nor the alternative hypothesis.

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b

The probability of making a Type I error is denoted by

a. 1 - α.

b. β.

c. α.

d. 1 - β.

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c

Read the t statistic from the t distribution table and circle the correct answer. For a one-tailed test (lower tail) with 22 degrees of freedom at α = .05, the value of t =

a. 1.383.

b. -1.717.

c. -1.721.

d. -1.383.

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b

The average manufacturing work week in metropolitan Chattanooga was 40.1 hours last year. It is believed that the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are

a. H0: μ = 40.1     Ha: μ ≠ 40.1.

b. H0: μ < 40.1     Ha: μ ≥ 40.1.

c. H0: μ ≥ 40.1     Ha: μ < 40.1.

d. H0: μ > 40.1     Ha: μ ≤ 40.1.

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c

In a two-tailed hypothesis test, the area in each tail corresponding to the critical values is equal to

a. 2α.

b. α.

c. 1 - α/2.

d. α/2.

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d

Read the z statistic from the normal distribution table and circle the correct answer. For a one-tailed test (upper tail) at α = .0630, z =

a. 1.645.

b. 1.53.

c. 1.50.

d. 1.96.

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b

A machine produces parts on an assembly line for an automotive manufacturer. If a part is defective, it must be scrapped. Every hour, the manager takes a random sample of 15 parts to test whether the process is "out of control" (i.e., to test whether the average proportion of defective parts exceeds 10%). Which of the following is a Type I error for this situation?

a. A Type I error for this situation would be to conclude that an out of control process is in control.

b. A Type I error for this situation would be to incorrectly conclude that the process is out of control.

c. A Type I error for this situation would be to correctly conclude that the process is in control.

d. A Type I error for this situation would be to conclude that an out of control process is out of control.

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b

A machine produces parts on an assembly line for an automotive manufacturer. If a part is defective, it must be scrapped. Every hour, the manager takes a random sample of 15 parts to test whether the process is "out of control" (i.e., to test whether the average proportion of defective parts exceeds 10%). Which of the following is a Type I error for this situation?

a. A Type I error for this situation would be to conclude that an out of control process is in control.

b. A Type I error for this situation would be to incorrectly conclude that the process is out of control.

c. A Type I error for this situation would be to correctly conclude that the process is in control.

d. A Type I error for this situation would be to conclude that an out of control process is out of control.

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b

A machine produces parts on an assembly line for an automotive manufacturer. If a part is defective, it must be scrapped. Every hour, the manager takes a random sample of 15 parts to test whether the process is "out of control" (i.e., to test whether the average proportion of defective parts exceeds 10%). Which of the following is a Type I error for this situation?

a. A Type I error for this situation would be to conclude that an out of control process is in control.

b. A Type I error for this situation would be to incorrectly conclude that the process is out of control.

c. A Type I error for this situation would be to correctly conclude that the process is in control.

d. A Type I error for this situation would be to conclude that an out of control process is out of control.

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b

In a two-tailed hypothesis test, the area in each tail corresponding to the critical values is equal to

a. α.

b. α/2.

c. 2α.

d. 1 - α/2.

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b

A school's newspaper reported that the proportion of students majoring in business is at least 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is

a. H0: p ≤ .30    Ha: p > .30.

b. H0: p < .30    Ha: p ≥ .30.

c. H0: p > .30    Ha: p ≤ .30.

d. H0: p ≥ .30    Ha: p < .30.

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d

In a two-tailed hypothesis test situation, the test statistic is determined to be t = -2.692. The sample size has been 45. The p-value for this test is

a. -.01.

b. +.01.

c. -.005.

d. +.005.

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Correct Response

b

A grocery store has an average sales of $8000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8300 per day. From past information, it is known that the standard deviation of the population is $1200. The correct null hypothesis for this problem is

a. μ = 8000.

b. μ ≤ 8300.

c. μ > 8300.

d. μ ≤ 8000.

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d

A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. The test statistic is

a. 1.96.

b. .05.

c. 2.00.

d. 1.65.

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c

A sample of 1400 items had 280 defective items. For the following hypothesis test,

H0: p ≤ .20
Ha: p > .20

the test statistic is

a. .14.

b. .20.

c. .28.

d. zero.

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d

Batteries produced by a manufacturing company have had a life expectancy of 135 hours. Because of an improved production process, the company believes that there has been an increase in the life expectancy of its batteries. A sample of 42 batteries showed an average life of 140 hours. From past information, the standard deviation of the population is known to be 24 hours. Test to determine whether there has been an increase in the life expectancy of batteries. What is the test statistic, and what conclusion can be made at the .10 level of significance?

a. z = 1.35; Reject the null hypothesis

b. z = .208; Do not reject the null hypothesis

c. z = .088; Do not reject the null hypothesis

d. z = 2.33; Reject the null hypothesis

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a

For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test,

a. will result in the area corresponding to the critical value being larger.

b. will result in the area corresponding to the critical value being smaller.

c. will have no effect on the area corresponding to the critical value.

d. Not enough information is given to answer this question.

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b

For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test,

a. will result in the area corresponding to the critical value being larger.

b. will result in the area corresponding to the critical value being smaller.

c. will have no effect on the area corresponding to the critical value.

d. Not enough information is given to answer this question.

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b

For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test,

a. will result in the area corresponding to the critical value being larger.

b. will result in the area corresponding to the critical value being smaller.

c. will have no effect on the area corresponding to the critical value.

d. Not enough information is given to answer this question.

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b

The standard error of x̄1 - x̄2 is the

a. pooled estimator of x̄1 - x̄2.

b. variance of the sampling distribution of x̄1 - x̄2.

c. standard deviation of the sampling distribution of x̄1 - x̄2.

d. margin of error of x̄1 - x̄2.

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c

Regarding inferences about the difference between two population means, the sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on

a. pooled samples.

b. research samples.

c. conditional samples.

d. independent samples.

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d

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information.

	Today	Five Years Ago
x̄	82	88
σ2	112.5	54
n	45	36

The standard error of x̄1 - x̄2 is

a. 12.9.

b. 4.

c. 9.3.

d. 2.

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d

The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information.

	Store's Card	Major Credit Card
Sample size	64	49
Sample mean	$140	$125
Population standard deviation	$10	$8

At 95% confidence, the margin of error is

a. 1.694.

b. 1.96.

c. 15.

d. 3.32.

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d

The following information was obtained from independent random samples. Suppose we are interested in testing H0: µ1 – µ2 = 15 and Ha: µ1 – µ2 ≠ 15.

What is the test statistic used in the hypothesis test for the difference between the two population means?

a. –5.49

b. 14.07

c. –1.37

d. .829

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a

The following information was obtained from independent random samples taken of two populations.
Assume normally distributed populations with equal variances.

	Sample 1	Sample 2
Sample Mean	45	42
Sample Variance	85	90
Sample Size	10	12

The degrees of freedom for the t distribution are

a. 22.

b. 20.

c. 21.

d. 24.

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b

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as

a. pooled samples.

b. independent samples.

c. corresponding samples.

d. matched samples.

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d

A researcher is interested in determining whether the mean of group 1 is 10 units larger than the mean of group 2. Which of the following represents the alternative hypothesis for testing the researcher's theory?

a. Ha: µ1 – µ2 > 10

b. Ha:µ1 – µ2 = 0

c. Ha: µ 1 – µ2 ≤ 10

d. Ha: µ1 = µ2

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a

A researcher is interested in determining whether the mean of group 1 is 10 units larger than the mean of group 2. Which of the following represents the alternative hypothesis for testing the researcher's theory?

a. Ha: µ1 – µ2 > 10

b. Ha:µ1 – µ2 = 0

c. Ha: µ 1 – µ2 ≤ 10

d. Ha: µ1 = µ2

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a

The following information was obtained from independent random samples taken of two populations.
Assume normally distributed populations with equal variances.

	Sample 1	Sample 2
Sample Mean	45	42
Sample Variance	85	90
Sample Size	10	12

The degrees of freedom for the t distribution are

a. 22.

b. 21.

c. 20.

d. 24.

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c

The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed.

Individual	Method 1	Method 2
1	7	5
2	5	9
3	6	8
4	7	7
5	5	6

If the null hypothesis H0: μd = 0 is tested at the 5% level,

a. the null hypothesis should not be rejected.

b. the null hypothesis should be revised.

c. the null hypothesis should be rejected.

d. the alternative hypothesis should be revised.

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a

Salary information regarding male and female employees of a large company is shown below.

	Male	Female
Sample Size	64	36
Sample Mean Salary (in $1000)	44	41
Population Variance (σ2)	128	72

The standard error of the difference between the two sample means is

a. 2.0.

b. 4.

c. 7.46.

d. 4.24.

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a

The following information was obtained from matched samples:

If the null hypothesis tested is H0: µd = 0, what is the test statistic for the difference between the two population means?

a. –.24

b. –.50

c. .51

d. –.48

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d

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed.

Driver	Manufacturer A	Manufacturer B
1	32	28
2	27	22
3	26	27
4	26	24
5	25	24
6	29	25
7	31	28
8	25	27

The test statistic is

a. 1.906.

b. 1.616.

c. 2.256.

d. 2.096.

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c

Two independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the

a. t distribution with 60 degrees of freedom.

b. t distribution with 58 degrees of freedom.

c. t distribution with 59 degrees of freedom.

d. t distribution with 61 degrees of freedom.

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b

Two independent types of a product were produced. The dollar amount of sales for each type over a one-month period was recorded. Assume the sales values are normally distributed. The results are given in the table below.

What are the p-value and conclusion for the hypothesis test of H0: µ1 – µ2 = 0 vs. Ha: µ1 – µ2 < 0 using α = 0.05?

a. p = 1.326; Do not reject H0.

b. p = .0924; Do not reject H0.

c. p = .0924; Reject H0.

d. p = 0; Reject H0.

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b

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.

Under Age of 18	Over Age of 18
n1 = 500	n2 = 600
Number of accidents = 180	Number of accidents = 150

We are interested in determining if the accident proportions differ between the two age groups. The p-value is

a. less than .001.

b. .3.

c. more than .10.

d. .0228.

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a

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed.

Driver	Manufacturer A	Manufacturer B
1	32	28
2	27	22
3	26	27
4	26	24
5	25	24
6	29	25
7	31	28
8	25	27

The mean of the differences is

a. .5.

b. 2.0.

c. 1.5.

d. 2.5.

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b

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed.

Driver	Manufacturer A	Manufacturer B
1	32	28
2	27	22
3	26	27
4	26	24
5	25	24
6	29	25
7	31	28
8	25	27

The mean of the differences is

a. .5.

b. 2.0.

c. 1.5.

d. 2.5.

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b

Production output (i.e., number of parts) for a random sample of days from two different plants is shown below.

What is the estimate of the standard deviation for the difference between the two means?

a. 75

b. 5.12

c. 14.66

d. 130.34

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b

A school administrator is interested in determining whether the proportion of students in the elementary school who are girls (pE) is significantly more than the proportion of students in the high school who are girls (pH). Which set of hypotheses would be most appropriate for answering the administrator's question?

a. H0 : pE – pH ≤ 0     Ha : pE – pH > 0

b. H0 : pE – pH = 0     Ha : pE – pH ≠ 0

c. H0: pE – pH < 0     Ha: pE – pH ≥ 0

d. H0 : pE – pH ≥ 0     Ha : pE – pH < 0

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a

The results of a recent poll on the preference of shoppers regarding two products are shown below.

Product	Shoppers Surveyed	Shoppers Favoring This Product
A	800	560
B	900	612

The point estimate for the difference between the two population proportions in favor of this product is

a. .44.

b. .07.

c. .68.

d. .02.

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d

An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.

Under Age of 18	Over Age of 18
n1 = 500	n2 = 600
Number of accidents = 180	Number of accidents = 150

We are interested in determining if the accident proportions differ between the two age groups. The p-value is

a. .3.

b. less than .001.

c. more than .10.

d. .0228.

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b

Generally, the ________ sample procedure for inferences about two population means provides better precision than the _______ sample approach.

a. single, independent

b. independent, pooled

c. matched, independent

d. matched, pooled

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c

The sampling distribution of p̄1 - p̄2 is approximated by a normal distribution if _____ are all greater than or equal to 5.

a. n1p2, n1(1 - p2), n2p1, n2(1 - p1)

b. n1p1, p1(1 - n1), n2p2, p2(1 - n2)

c. n1p2, p2(1 - n2), n2p1, p1(1 - n1)

d. n1p1, n1(1 - p1), n2p2, n2(1 - p2)

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d

Which of the following is not true with respect to tests for the difference between two means when the population standard deviations are known?

a. The samples must come from normally distributed populations or the sample sizes must be large enough to apply the central limit theorem.

b. The margin of error for a confidence interval estimate is .

c. The samples must be randomly and independently selected.

d. The test statistic for a hypothesis test has a t distribution.

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d

The following information was obtained from independent random samples taken of two populations.
Assume normally distributed populations with equal variances.

	Sample 1	Sample 2
Sample Mean	45	42
Sample Variance	85	90
Sample Size	10	12

The 95% confidence interval for the difference between the two population means is (use rounded standard error)

a. -4.86 to 10.86.

b. -5.344 to 11.344.

c. -2.65 to 8.65.

d. -5 to 3.

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b

Salary information regarding male and female employees of a large company is shown below.

	Male	Female
Sample Size	64	36
Sample Mean Salary (in $1000)	44	41
Population Variance (σ2)	128	72

The standard error of the difference between the two sample means is

a. 7.46.

b. 4.24.

c. 4.

d. 2.0.

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d

Salary information regarding male and female employees of a large company is shown below.

	Male	Female
Sample Size	64	36
Sample Mean Salary (in $1000)	44	41
Population Variance (σ2)	128	72

The standard error of the difference between the two sample means is

a. 7.46.

b. 4.24.

c. 4.

d. 2.0.

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d

 A simple random sample of 64 observations was taken from a large population. The sample mean and the standard deviation were determined to be 320 and 120 respectively. The standard error of the mean is

a. 40

b. 15

c. 1.875

d. 5

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b

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. The mean and the standard deviation of the sampling distribution of the sample means are

a. 36 and 1.86.

b. 8.7 and 1.94.

c. 36 and 8.

d. 36 and 1.94.

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a

How many simple random samples of size 5 can be selected from a population of size 8?

a. 336

b. 56

c. 40

d. 68

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b

A sample of 66 observations will be taken from an infinite population. The population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is

a. 0.0778

b. 0.9222

c. 0.0568

d. 0.4222

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b

The following information was collected from a simple random sample of a population.

16

19

18

17

20

18

The point estimate of the mean of the population is

a. 16

b. 108

c. 19.6

d. 18.0

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d

Random samples of size 100 are taken from an infinite population whose population proportion is 0.2. The mean and standard deviation of the sample proportion are

a. 0.2 and 0.2

b. 20 and .04

c. 0.2 and .04

d. 20 and 0.2

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c

The sample statistic, such as x̄, s, or p̄, that provides the point estimate of the population parameter is known as

a. a population parameter.

b. a point estimator.

c. a parameter.

d. a population statistic.

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b

The standard deviation of p̄ is referred to as the

a. deviated proportion.

b. sample mean proportion.

c. standard error of the proportion.

d. standard proportion.

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c

A sample of 25 observations is taken from an infinite population. The sampling distribution of p̄ is

a. not normal since n < 30

b. approximately normal if np > 30 and n(1-P) > 30

c. approximately normal because p̄ is always normally distributed

d. approximately normal if np ≥ 5 and n(1-P) ≥ 5

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d

In point estimation

a. the mean of the population equals the mean of the sample.

b. data from the sample is used to estimate the sample statistic.

c. data from the sample is used to estimate the population parameter.

d. data from the population is used to estimate the population parameter.

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c

In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is

a. .871 to .929.

b. .071 to .129.

c. .765 to .835.

d. .120 to .280.

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b

When constructing a confidence interval for the population mean using the standard deviation of the sample, the degrees of freedom for the t distribution equals

a. n + 1.

b. 2n.

c. n.

d. n - 1.

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d

To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures are recommended when σ is unknown except

a. use the estimated σ from a previous study.

b. use the sample standard deviation from a preliminary sample.

c. use judgment or a best guess.

d. use .5 as an estimate.

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d

If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient will be

a. 1.645.

b. .95.

c. .485.

d. 1.96.

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b

A 95% confidence interval for a population mean is determined to be 100 to 120. For the same data, if the confidence coefficient is reduced to .90, the confidence interval for μ

a. becomes 100.1 to 120.1.

b. becomes wider.

c. does not change.

d. becomes narrower.

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d

A random sample of 30 varieties of cereal was selected. The average number of calories per serving for these cereals is  = 120. Assuming that σ = 10, find a 95% confidence interval for the mean number of calories, μ, in a serving of cereal.

a. 117.00 to 123.00

b. 116.42 to 123.58

c. 115.30 to 124.70

d. 118.00 to 122.00

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b

We are interested in conducting a study in order to determine the percentage of voters in a city who would vote for the incumbent mayor. What is the minimum sample size needed to estimate the population proportion with a margin of error not exceeding 4% at 95% confidence?

a. 600

b. 601

c. 625

d. 626

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b

A machine that produces a major part for an airplane engine is monitored closely. In the past, 10% of the parts produced would be defective. With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is

a. 111.

b. 216.

c. 110.

d. 217.

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d

We can use the normal distribution to make confidence interval estimates for the population proportion, p, when

a. both np ≥ 5 and n(1 - p) ≥ 5.

b. n(1 - p) ≥ 5.

c. p has a normal distribution.

d. np ≥ 5.

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a

The t distribution should be used whenever

a. the sample standard deviation is used to estimate the population standard deviation.

b. the population standard deviation is known.

c. the population is not normally distributed.

d. the sample size is less than 30.

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a

A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The probability that the sample mean will be greater than 57.95 is

a. .0495

b. .9505

c. .4505

d. 0

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a

Whenever the population has a normal probability distribution, the sampling distribution of x̄ is a normal probability distribution for

a. any sample size.

b. small sample sizes.

c. large sample sizes.

d. samples of size thirty or greater.

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a

A simple random sample of 64 observations was taken from a large population. The sample mean and the standard deviation were determined to be 320 and 120 respectively. The standard error of the mean is

a. 15

b. 40

c. 1.875

d. 5

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a

A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is

a. 0.9511

b. 0.7200

c. 8.3600

d. 0.0347

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a

The population being studied is usually considered ______ if it involves an ongoing process that makes listing or counting every element in the population impossible.

a. infinite

b. finite

c. symmetric

d. skewed

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a

Which of the following is an example of nonprobabilistic sampling?

a. Stratified simple random sampling

b. Judgment sampling

c. Cluster sampling

d. Simple random sampling

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b

In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. The standard deviation of p̄, known as the standard error of the proportion is approximately

a. 5.477

b. 0.05477

c. 54.77

d. 0.5477

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b

Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and 100 said "no". The point estimate of the proportion in the population who will respond "no" is

a. 75

b. 0.50

c. 0.25

d. 0.75

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c

A wildlife management organization is interested in estimating the number of moose in a particular region. Organization employees divide the region into 10 sections and randomly select four sections to survey the number of moose present. What sampling method is being used?

a. Systematic sampling

b. Stratified random sampling

c. Cluster sampling

d. Judgment sampling

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c

A population of size 1,000 has a proportion of 0.5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are

a. 500 and 0.050

b. 0.5 and 0.047

c. 0.5 and 0.050

d. 500 and 0.047

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b

The sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is

a. 117.

b. 11.

c. 10.

d. 116.

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a

When s is used to estimate σ, the margin of error is computed by using the

a. t distribution.

b. normal distribution.

c. mean of the population.

d. mean of the sample.

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a

The manager of a department store wants to determine the proportion of customers who use the store's credit card when making a purchase. What sample size should he select so that at 96% confidence the error will not be more than 10%?

a. 106

b. 76

c. 1

d. There is not enough information given to determine the sample size.

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a

In an interval estimation for a proportion of a population, the value of z at 99.2% confidence is

a. 2.41.

b. 2.65.

c. 1.96.

d. 1.645.

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b

What is the t value for  and 15 degrees of freedom?

a. 2.145

b. 0.691

c. 2.120

d. 2.131

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d

In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is

a. .120 to .280.

b. .871 to .929.

c. .071 to .129.

d. .765 to .835.

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c

An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the

a. interval estimate.

b. confidence level.

c. margin of error.

d. point estimate.

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a

From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the

a. t distribution with 24 degrees of freedom.

b. t distribution with 25 degrees of freedom.

c. t distribution with 26 degrees of freedom.

d. normal distribution.

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a

A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. The standard error of the mean is

a. 80.83.

b. 7.0.

c. 1.611.

d. .8083.

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d

The t distribution should be used whenever

a. the population is not normally distributed.

b. the sample size is less than 30.

c. the sample standard deviation is used to estimate the population standard deviation.

d. the population standard deviation is known.

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c

Which of the following best describes the form of the sampling distribution of the sample proportion?

a. When standardized, it is the t distribution.

b. When standardized, it is exactly the standard normal distribution.

c. It is approximately normal as long as n ≥ 30.

d. It is approximately normal as long as np ≥ 5 and n(1 - p) ≥ 5.

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d

A sample of 66 observations will be taken from an infinite population. The population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is

a. 0.0778

b. 0.4222

c. 0.9222

d. 0.0568

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c

A wildlife management organization is interested in estimating the number of moose in a particular region. Organization employees divide the region into 10 sections and randomly select four sections to survey the number of moose present. What sampling method is being used?

a. Systematic sampling

b. Cluster sampling

c. Stratified random sampling

d. Judgment sampling

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b

It is impossible to construct a frame for a(n)

a. finite population.

b. infinite population.

c. target population.

d. defined population.

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b

A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is

a. 0.9511

b. 8.3600

c. 0.0347

d. 0.7200

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a

A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were female. The standard error of the proportion is

a. 0.0016

b. 0.1600

c. 0.0400

d. 0.2400

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c

A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is

a. 0.9332.

b. 0.0668.

c. 0.4332.

d. 0.9544.

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d

As a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever

a. np ≥5, n ≥30.

b. n ≥ 30 and (1 - p) = 0.5.

c. np ≥5 and n(1-p) ≥5.

d. None of these alternatives are correct.

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c

Random samples of size 36 are taken from an infinite population whose mean and standard deviation are 20 and 15, respectively. The distribution of the population is unknown. The mean and the standard error of the mean are

a. 20 and 15

b. 20 and 0.417

c. 36 and 15

d. 20 and 2.5

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d

The number of simple random samples of size 20 that can be selected from a finite population of size 25 is _____.

a. 53,130

b. 1

c. 120

d. 20

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a

If we consider the simple random sampling process as an experiment, the sample mean is

a. always zero.

b. exactly equal to the population mean.

c. a random variable.

d. always smaller than the population mean.

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c

Which of the following is an example of nonprobabilistic sampling?

a. Cluster sampling

b. Simple random sampling

c. Judgment sampling

d. Stratified simple random sampling

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c

The sampling distribution of the sample means

a. is used as a point estimator of the population mean μ.

b. is an unbiased estimator.

c. is the probability distribution showing all possible values of the sample mean.

d. shows the distribution of all possible values of μ.

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c

A sample of 240 is selected from a finite population of 500. If the standard deviation of the population is 44, what is the standard error of the sample mean?

a. 1.42

b. 2.84

c. 2.05

d. 4.20

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b

Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and 100 said "no". The point estimate of the proportion in the population who will respond "yes" is

a. 0.25

b. approximately 300

c. 300

d. 0.75

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d

In point estimation

a. data from the population is used to estimate the population parameter.

b. data from the sample is used to estimate the sample statistic.

c. the mean of the population equals the mean of the sample.

d. data from the sample is used to estimate the population parameter.

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d

A population of size 1,000 has a proportion of 0.5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are

a. 0.5 and 0.047

b. 500 and 0.047

c. 500 and 0.050

d. 0.5 and 0.050

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a

The probability distribution of all possible values of the sample mean x̄ is

a. the sampling distribution of x̄.

b. the probability density function of x̄.

c. one, since it considers all possible values of the sample mean.

d. the grand mean, since it considers all possible values of the sample mean.

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a

The population being studied is usually considered ______ if it involves an ongoing process that makes listing or counting every element in the population impossible.

a. symmetric

b. skewed

c. finite

d. infinite

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d

A population of size 320 has a proportion equal to .60 for the characteristic of interest. What are the mean and the standard deviation, respectively, of the sample proportion for samples of size 12?

a. .60 and .02

b. 320 and .02

c. 192 and 45

d. .60 and .14

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d

From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population (μ).

a. The normal distribution can be used.

b. The sample size must be increased.

c. The t distribution with 5 degrees of freedom must be used.

d. The t distribution with 6 degrees of freedom must be used.

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b

If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient will be

a. .485.

b. 1.96.

c. .95.

d. 1.645.

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c

When s is used to estimate σ, the margin of error is computed by using the

a. t distribution.

b. normal distribution.

c. mean of the sample.

d. mean of the population.

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a

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the

a. margin of error.

b. proportion estimate.

c. same as α.

d. confidence coefficient.

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c

A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is

a. 8.225.

b. 9.92.

c. 9.8.

d. 8.3.

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c

A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. If we want to determine a 95% confidence interval for the average hourly income of the population, the value of t is

a. 1.28.

b. 1.645.

c. 1.96.

d. 1.993.

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d

A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. The standard error of the mean is

a. 7.0.

b. 80.83.

c. 1.611.

d. .8083.

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d

To compute the minimum sample size for an interval estimate of μ, we must first determine all of the following except

a. population standard deviation.

b. degrees of freedom.

c. confidence level.

d. desired margin of error.

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b

A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. The value of the margin of error at 95% confidence is

a. 7.00.

b. .81.

c. 1.61.

d. 80.83.

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c

A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. The 95% confidence interval for the average hourly wage (in $) of all information system managers is

a. 39.40 to 42.10.

b. 37.54 to 43.96.

c. 38.61 to 42.89.

d. 39.14 to 42.36.

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d

The following random sample from a population whose values were normally distributed was collected.

10

8

11

11

The 95% confidence interval for μ is

a. 7.75 to 12.25.

b. 8.00 to 10.00.

c. 9.25 to 10.75.

d. 8.52 to 11.48.

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a

To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures are recommended when σ is unknown except

a. use the sample standard deviation from a preliminary sample.

b. use judgment or a best guess.

c. use .5 as an estimate.

d. use the estimated σ from a previous study.

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c

A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The 98% confidence interval for the true average age of all students in the university is

a. 24.4 to 25.6.

b. 23.0 to 27.0.

c. 20.0 to 30.0.

d. 20.5 to 29.5.

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a

Using an α = .04, a confidence interval for a population proportion is determined to be .65 to .75. For the same data, if α is decreased, the confidence interval for the population proportion

a. remains the same.

b. uses a zero margin of error.

c. becomes narrower.

d. becomes wider.

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d

The degrees of freedom associated with a t distribution are a function of the

a. area in the upper tail.

b. confidence coefficient.

c. sample size.

d. sample standard deviation.

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c

Using α = 0.05, a confidence interval for a population proportion is determined to be 0.15 to 0.35. If the level of significance is increased, the interval for the population proportion

a. becomes narrower.

b. becomes wider.

c. does not change.

d. Not enough information is provided to answer this question.

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a

The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the

a. standard deviation.

b. degrees of freedom.

c. finite correction factor.

d. sample size.

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b

A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. The t value needed to develop the 95% confidence interval for the population mean SAT score is

a. 1.96.

b. 1.645.

c. 1.998.

d. 1.28.

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c

Which of the following must be decided by the researcher when computing the minimum sample size for an interval estimate of μ or p?

a. Mean

b. Margin of error

c. Degrees of freedom

d. Standard deviation

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b

We can use the normal distribution to make confidence interval estimates for the population proportion, p, when

a. both np ≥ 5 and n(1 - p) ≥ 5.

b. p has a normal distribution.

c. np ≥ 5.

d. n(1 - p) ≥ 5.

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a

A sample statistic is an unbiased estimator of the population parameter when

a. the standard deviation of the sampling distribution is less than 5.

b. the expected value of the sample statistic is equal to the value of the population parameter.

c. the data was used to estimate a population mean.

d. the mean of the sampling distribution has a z-score of zero.

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b

The expected value of equals the mean of the population from which the sample is drawn

a. only if the sample size is 30 or greater.

b. for any sample size.

c. only if the sample size is 100 or greater.

d. only if the sample size is 50 or greater.

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b

A probability sampling method in which we randomly select one of the first k elements and then select every k th element thereafter is

a. systematic sampling.

b. cluster sampling.

c. convenience sampling.

d. stratified random sampling.

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a

Which of the following is(are) point estimator(s)?

a. μ

b. σ

c. α

d. s

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d

A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is

a. 8.3600

b. 0.0347

c. 0.9511

d. 0.7200

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c

A simple random sample of 5 observations from a population containing 400 elements was taken, and the following values were obtained.

12

18

19

20

21

A point estimate of the mean is

a. 10

b. 400

c. 18

d. 20

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c

Suppose candidate A for a town council seat receives 43% of the votes in an election. As voters leave the polls, they are asked who they voted for. What is the probability that less than 40% of the 80 voters surveyed indicate they voted for candidate A? Assume an infinite population.

a. .1368

b. .8632

c. .2939

d. .7061

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c

Suppose the salaries of university professors are approximately normally distributed with a mean of $65,000 and a standard deviation of $7,000. If a random sample of size 25 is taken and the mean is calculated, what is the probability that the mean value will be between $62,500 and $64,000?

a. .2005

b. .1465

c. .0827

d. .0371

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a

In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. The standard deviation of p̄, known as the standard error of the proportion is approximately

a. 0.5477

b. 5.477

c. 54.77

d. 0.05477

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d

A probability distribution of all possible values of a sample statistic is known as

a. a parameter.

b. a sampling distribution.

c. a sample statistic.

d. simple random sampling.

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b

A population consists of 8 items. The number of different simple random samples of size 3 that can be selected from this population is

a. 56

b. 128

c. 24

d. 512

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a

The following information was collected from a simple random sample of a population.

16

19

18

17

20

18

The point estimate of the population standard deviation is

a. 1.667

b. 1.414

c. 2.000

d. 1.291

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b

In point estimation

a. data from the population is used to estimate the population parameter.

b. the mean of the population equals the mean of the sample.

c. data from the sample is used to estimate the sample statistic.

d. data from the sample is used to estimate the population parameter.

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d

A wildlife management organization is interested in estimating the number of moose in a particular region. Organization employees divide the region into 10 sections and randomly select four sections to survey the number of moose present. What sampling method is being used?

a. Stratified random sampling

b. Systematic sampling

c. Judgment sampling

d. Cluster sampling

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d

The number of simple random samples of size 20 that can be selected from a finite population of size 25 is _____.

a. 120

b. 1

c. 53,130

d. 20

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c

The purpose of statistical inference is to provide information about the

a. mean of the sample based upon the mean of the population.

b. population based upon information contained in the sample.

c. population based upon information contained in the population.

d. sample based upon information contained in the population.

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b

Cluster sampling is

a. a nonprobability sampling method.

b. the same as convenience sampling.

c. a systematic sampling method.

d. a probability sampling method.

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d

A single numerical value used as an estimate of a population parameter is known as

a. a parameter.

b. a point estimate.

c. a mean estimator.

d. a population parameter.

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b

If we select simple random samples of size 2 from the given data, what is the probability of any of the five employees being selected first?

a. .50

b. .40

c. .10

d. .20

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d

The extent of the sampling error might be affected by all of the following factors except

a. the variability of the population.

b. the expected value of the sample statistic.

c. the sample size.

d. the sampling method used.

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b

In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. If the sample mean is 9 hours, then the 95% confidence interval is

a. 7.36 to 10.64 hours.

b. 7.04 to 10.96 hours.

c. 7.80 to 10.20 hours.

d. 8.61 to 9.39 hours.

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d

A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The 98% confidence interval for the true average age of all students in the university is

a. 23.0 to 27.0.

b. 20.5 to 29.5.

c. 20.0 to 30.0.

d. 24.4 to 25.6.

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d

A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is

a. 15.2 to 24.8.

b. 19.20 to 20.80.

c. 21.2 to 22.8.

d. 19.216 to 20.784.

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b

In order to estimate the average electric usage per month, a sample of 81 houses was selected and the electric usage was determined. Assume a population standard deviation of 450 kilowatt-hours. If the sample mean is 1858 kWh, the 95% confidence interval estimate of the population mean is

a. 1776 to 1940 kWh.

b. 1729 to 1987 kWh.

c. 1758 to 1958 kWh.

d. 1760 to 1956 kWh.

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d

A 95% confidence interval and a 99% confidence interval are computed from the same set of data. Which of the following statements is correct?

a. The intervals have the same width.

b. You need to know the sample size, n, and the standard deviation to determine which interval is wider.

c. The 99% confidence interval is wider.

d. The 95% confidence interval is wider.

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c

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

a. fluctuates.

b. stays the same.

c. becomes smaller.

d. becomes larger.

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c

A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. The 95% confidence interval for the population mean SAT score is

a. 1340.06 to 1459.94.

b. 1320.32 to 1479.68.

c. 1341.20 to 1458.80.

d. 1349.93 to 1450.07.

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a

Using α = 0.05, a confidence interval for a population proportion is determined to be 0.15 to 0.35. If the level of significance is increased, the interval for the population proportion

a. becomes narrower.

b. becomes wider.

c. does not change.

d. Not enough information is provided to answer this question.

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a

Which of the following is not required when computing the sample size for an interval estimate of the population mean?

a. Population mean

b.

c. Margin of error the researcher is willing to accept

d. Population standard deviation

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a

A random sample of 15 employees was selected. The average age in the sample was 31 years with a variance of 49 years. Assuming ages are normally distributed, the 98% confidence interval for the population average age is _____.

a. 25.62 to 36.38

b. 27.82 to 34.18

c. 11.54 to 18.46

d. 26.26 to 35.74

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d

A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is

a. 8.225.

b. 9.92.

c. 9.8.

d. 8.3.

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c

The t distribution should be used whenever

a. the sample size is less than 30.

b. the population is not normally distributed.

c. the sample standard deviation is used to estimate the population standard deviation.

d. the population standard deviation is known.

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c

We are interested in conducting a study to determine the percentage of voters of a state would vote for the incumbent governor. What is the minimum sample size needed to estimate the population proportion with a margin of error of .05 or less at 95% confidence?

a. 200.

b. 385.

c. 58.

d. 100.

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b

If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the

a. width of the confidence interval to decrease.

b. width of the confidence interval to remain the same.

c. width of the confidence interval to increase.

d. sample size to increase.

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c

In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. With a .95 probability, the margin of error is approximately

a. .39.

b. 1.64.

c. 1.96.

d. .20.

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a

In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. If the sample mean is 9 hours, then the 95% confidence interval is

a. 7.36 to 10.64 hours.

b. 7.04 to 10.96 hours.

c. 7.80 to 10.20 hours.

d. 8.61 to 9.39 hours.

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d

As the degrees of freedom increase, the t distribution approaches the

a. exponential distribution.

b. p distribution.

c. normal distribution.

d. uniform distribution.

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c

In which of the following situations should the t distribution be used?

a. When the sample standard deviation is used to estimate the population standard deviation

b. When the sample size is less than 30

c. When the population is not normally distributed

d. Only when the population mean is 0

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a

The following random sample from a population whose values were normally distributed was collected.

10

8

11

11

The 95% confidence interval for μ is

a. 7.75 to 12.25.

b. 9.25 to 10.75.

c. 8.52 to 11.48.

d. 8.00 to 10.00.

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a

It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is

a. 189.

b. 190.

c. 74.

d. 75.

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d

The sampling error is the

a. same as the standard error of the mean.

b. error caused by selecting a bad sample.

c. difference between the value of the sample mean and the value of the population mean.

d. standard deviation multiplied by the sample size.

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c

A probability distribution of all possible values of a sample statistic is known as

a. a sampling distribution.

b. a sample statistic.

c. a parameter.

d. simple random sampling.

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a

A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 80 and 12 respectively. The standard error of the mean is

a. 8.00

b. 0.80

c. 0.12

d. 1.20

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d

Doubling the size of the sample will

a. reduce the standard error of the mean to approximately 70% of its current value.

b. have no effect on the standard error of the mean.

c. reduce the standard error of the mean to one-half its current value.

d. double the standard error of the mean.

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a

The standard error of the proportion will become larger as

a. n increases.

b. p approaches .5.

c. p approaches 1.

d. p approaches 0.

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b

In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. The standard deviation of p̄, known as the standard error of the proportion is approximately

a. 5.477

b. 0.5477

c. 54.77

d. 0.05477

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Solution

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d

The closer the sample mean is to the population mean,

a. the smaller the sampling error.

b. the larger the sampling error.

c. the sampling error equals 1.

d. None of these alternatives are correct.

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a

The probability distribution of all possible values of the sample mean x̄ is

a. the grand mean, since it considers all possible values of the sample mean.

b. the sampling distribution of x̄.

c. one, since it considers all possible values of the sample mean.

d. the probability density function of x̄.

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b

From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximately

a. 2

b. 30

c. 1.1022

d. 1.4847

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d

It is impossible to construct a frame for a(n)

a. finite population.

b. infinite population.

c. target population.

d. defined population.

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Solution

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b

From a population of 200 elements, a sample of 49 elements is selected. It is determined that the sample mean is 56 and the sample standard deviation is 14. The standard error of the mean is

a. 3

b. greater than 2

c. 2

d. less than 2

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d

A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of x̄ is

a. approximately normal because of the central limit theorem.

b. normal if the population is normally distributed.

c. approximately normal because x̄ is always approximately normally distributed.

d. approximately normal because the sample size is large in comparison to the population size.

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b

A population of size 1,000 has a proportion of 0.5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are

a. 0.5 and 0.050

b. 0.5 and 0.047

c. 500 and 0.047

d. 500 and 0.050

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b

The following information was collected from a simple random sample of a population.

16

19

18

17

20

18

The point estimate of the population standard deviation is

a. 1.667

b. 1.291

c. 1.414

d. 2.000

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c

For a population with any distribution, the form of the sampling distribution of the sample mean is

a. sometimes normal for all sample sizes.

b. sometimes normal for large sample sizes.

c. always normal for all sample sizes.

d. always normal for large sample sizes.

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d

Which of the following is an example of nonprobabilistic sampling?

a. Judgment sampling

b. Stratified simple random sampling

c. Cluster sampling

d. Simple random sampling

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a

As the sample size increases, the

a. population mean increases.

b. standard deviation of the population decreases.

c. standard error of the mean increases.

d. standard error of the mean decreases.

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d

The purpose of statistical inference is to provide information about the

a. population based upon information contained in the population.

b. sample based upon information contained in the population.

c. mean of the sample based upon the mean of the population.

d. population based upon information contained in the sample.

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d

A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. In this problem the 0.22 is

a. the standard error of the mean.

b. a statistic.

c. a parameter.

d. the average content of colognes in the long run.

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c

A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The probability that the sample mean will be between 183 and 186 is

a. 0.8185

b. 0.3413

c. 0.4772

d. 0.1359

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d

The following information was collected from a simple random sample of a population.

16

19

18

17

20

18

The point estimate of the population standard deviation is

a. 1.291

b. 1.667

c. 2.000

d. 1.414

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d

Suppose candidate A for a town council seat receives 43% of the votes in an election. As voters leave the polls, they are asked who they voted for. What is the probability that less than 40% of the 80 voters surveyed indicate they voted for candidate A? Assume an infinite population.

a. .8632

b. .2939

c. .7061

d. .1368

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b

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the sample mean will be larger than 82 is

a. 0.9772

b. 0.0228

c. 0.4772

d. 0.5228

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b

Cluster sampling is

a. a probability sampling method.

b. a nonprobability sampling method.

c. a systematic sampling method.

d. the same as convenience sampling.

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a

As the sample size increases, the

a. standard deviation of the population decreases.

b. standard error of the mean increases.

c. standard error of the mean decreases.

d. population mean increases.

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c

The population being studied is usually considered ______ if it involves an ongoing process that makes listing or counting every element in the population impossible.

a. infinite

b. symmetric

c. skewed

d. finite

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a

A finite population correction factor is needed in computing the standard deviation of the sampling distribution of sample means

a. whenever the sample size is more than 5% of the population size.

b. whenever the population is infinite.

c. irrespective of the size of the sample.

d. whenever the sample size is less than 5% of the population size.

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a

A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have

a. the same probability of being selected

b. a probability of 1/n of being selected

c. a probability of 1/N of being selected

d. a probability of N/n of being selected

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a

A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. In this problem the 0.22 is

a. a parameter.

b. the standard error of the mean.

c. the average content of colognes in the long run.

d. a statistic.

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a

A population of size 320 has a proportion equal to .60 for the characteristic of interest. What are the mean and the standard deviation, respectively, of the sample proportion for samples of size 12?

a. .60 and .02

b. .60 and .14

c. 320 and .02

d. 192 and 45

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b

A finite population correction factor is needed in computing the standard deviation of the sampling distribution of sample means

a. whenever the sample size is more than 5% of the population size.

b. whenever the sample size is less than 5% of the population size.

c. irrespective of the size of the sample.

d. whenever the population is infinite.

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a

A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have

a. a probability of 1/n of being selected

b. the same probability of being selected

c. a probability of 1/N of being selected

d. a probability of N/n of being selected

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b

In point estimation

a. data from the sample is used to estimate the sample statistic.

b. the mean of the population equals the mean of the sample.

c. data from the sample is used to estimate the population parameter.

d. data from the population is used to estimate the population parameter.

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c

The sample statistic, such as x̄, s, or p̄, that provides the point estimate of the population parameter is known as

a. a parameter.

b. a point estimator.

c. a population parameter.

d. a population statistic.

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b

All of the following are true about the standard error of the mean except

a. its value is influenced by the standard deviation of the population.

b. it measures the variability in sample means.

c. it decreases as the sample size increases.

d. it is larger than the standard deviation of the population.

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d

Which of the following best describes the form of the sampling distribution of the sample proportion?

a. It is approximately normal as long as np ≥ 5 and n(1 - p) ≥ 5.

b. When standardized, it is the t distribution.

c. When standardized, it is exactly the standard normal distribution.

d. It is approximately normal as long as n ≥ 30.

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a

The sampling distribution of the sample means

a. is used as a point estimator of the population mean μ.

b. shows the distribution of all possible values of μ.

c. is an unbiased estimator.

d. is the probability distribution showing all possible values of the sample mean.

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d

A sample of 51 observations will be taken from an infinite population. The population proportion equals 0.85. The probability that the sample proportion will be between 0.9115 and 0.946 is

a. 0.8633

b. 0.0345

c. 0.6900

d. 0.0819

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d

A sample of 66 observations will be taken from an infinite population. The population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is

a. 0.4222

b. 0.0778

c. 0.9222

d. 0.0568

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c

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 200 and 18, respectively. The distribution of the population is unknown. The mean and the standard error of the mean are

a. 200 and 2

b. 200 and 18

c. 81 and 18

d. 9 and 2

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a

The following data was collected from a simple random sample of a population.

13

15

14

16

12

If the population consisted of 10 elements, how many different random samples of size 6 could be drawn from the population?

a. 362880

b. 60

c. 210

d. 3024

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c

ampling distribution of x̄ is the

a. mean of the sample.

b. probability distribution of the sample proportion.

c. probability distribution of the sample mean.

d. mean of the population.

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c

The standard deviation of a point estimator is called the

a. point estimator.

b. variance of estimation.

c. standard deviation.

d. standard error.

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d

A sample of 400 observations will be taken from an infinite population. The population proportion equals 0.8. The probability that the sample proportion will be greater than 0.83 is

a. 0.9332

b. 0.4332

c. 0.5668

d. 0.0668

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d

A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of an element being selected is

a. 0.010

b. 0.100

c. 0.002

d. 0.001

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c

A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is

a. 0.7200

b. 8.3600

c. 0.0347

d. 0.9511

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d

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. The mean and the standard deviation of the sampling distribution of the sample means are

a. 36 and 1.86.

b. 36 and 8.

c. 8.7 and 1.94.

d. 36 and 1.94.

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a

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the sample mean will be larger than 82 is

a. 0.4772

b. 0.0228

c. 0.9772

d. 0.5228

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b

A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were female. The standard error of the proportion is

a. 0.0400

b. 0.2400

c. 0.0016

d. 0.1600

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a

A wildlife management organization is interested in estimating the number of moose in a particular region. Organization employees divide the region into 10 sections and randomly select four sections to survey the number of moose present. What sampling method is being used?

a. Judgment sampling

b. Cluster sampling

c. Systematic sampling

d. Stratified random sampling

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b

In which of the following situations should the t distribution be used?

a. When the population is not normally distributed

b. Only when the population mean is 0

c. When the sample size is less than 30

d. When the sample standard deviation is used to estimate the population standard deviation

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d

In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is

a. .871 to .929.

b. .071 to .129.

c. .120 to .280.

d. .765 to .835.

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b

When constructing a confidence interval for the population mean using the standard deviation of the sample, the degrees of freedom for the t distribution equals

a. n + 1.

b. 2n.

c. n.

d. n - 1.

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d

For a given confidence level and when σ is known, the margin of error in a confidence interval estimate

a. increases as the sample size increases.

b. is the same for all samples of the same size.

c. varies from sample to sample of the same size.

d. is independent of sample size.

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b

The ability of an interval estimate to contain the value of the population parameter is described by the

a. point estimate.

b. confidence level.

c. degrees of freedom.

d. precise value of the population mean μ.

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b

From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the

a. t distribution with 26 degrees of freedom.

b. normal distribution.

c. t distribution with 24 degrees of freedom.

d. t distribution with 25 degrees of freedom.

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c

To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except

a. use the sample proportion from a previous study.

b. use 1.0 as an estimate.

c. use judgment or a best guess.

d. use the sample proportion from a preliminary sample.

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b

In interval estimation, as the sample size becomes larger, the interval estimate

a. becomes narrower.

b. remains the same, because the mean is not changing.

c. becomes wider.

d. gets closer to 1.96.

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a

As the sample size increases, the margin of error

a. increases.

b. decreases.

c. fluctuates depending on the mean.

d. stays the same.

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b

A university planner wants to determine the proportion of undergraduate students who plan to attend graduate school. She surveys 54 current students and finds that 27 would like to continue their education in graduate school. Which of the following is the correct 90% confidence interval estimate for the proportion of undergraduates who plan to attend graduate school?

a. 0.50 to 0.75

b. 26.727 to 27.273

c. 0.3881 to 0.6119

d. 0.3608 to 0.6392

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c

The level of significance α

a. is (1 - confidence coefficient).

b. can be any positive value.

c. can be any value between -1.96 to 1.96.

d. is always a negative value.

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a

A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. If we want to determine a 95% confidence interval for the average hourly income of the population, the value of t is

a. 1.28.

b. 1.645.

c. 1.993.

d. 1.96.

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c

The use of the normal probability distribution as an approximation of the sampling distribution of p̄ is based on the condition that both np and n(1 - p) equal or exceed

a. .05.

b. 5.

c. 30.

d. 10.

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b

In a random sample of 144 observations, p̄ = .6. The 95% confidence interval for p is

a. .52 to .68.

b. .55 to .65.

c. .50 to .70.

d. .14 to .20.

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a

When s is used to estimate σ, the margin of error is computed by using the

a. mean of the sample.

b. mean of the population.

c. normal distribution.

d. t distribution.

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d

In developing an interval estimate, if the population standard deviation is unknown

a. the standard deviation is arrived at using the range.

b. it is impossible to develop the interval estimate.

c. the sample standard deviation must be used.

d. it is assumed that the population standard deviation is 1.

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c

A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The 98% confidence interval for the true average age of all students in the university is

a. 23.0 to 27.0.

b. 20.0 to 30.0.

c. 20.5 to 29.5.

d. 24.4 to 25.6.

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d

A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is

a. 8.3.

b. 9.8.

c. 8.225.

d. 9.92.

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b

A random sample of 30 varieties of cereal was selected. The average number of calories per serving for these cereals is  = 120. Assuming that σ = 10, find a 95% confidence interval for the mean number of calories, μ, in a serving of cereal.

a. 115.30 to 124.70

b. 118.00 to 122.00

c. 117.00 to 123.00

d. 116.42 to 123.58

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d

The degrees of freedom associated with a t distribution are a function of the

a. area in the upper tail.

b. confidence coefficient.

c. sample standard deviation.

d. sample size.

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d

The t distribution should be used whenever

a. the population is not normally distributed.

b. the sample standard deviation is used to estimate the population standard deviation.

c. the sample size is less than 30.

d. the population standard deviation is known.

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b

The manager of a retail store has taken a random sample of 50 customers. The average amount spent by these 50 customers was $110. It is known that the standard deviation of the amount spent by all customers is $10.60. If the confidence coefficient is increased from 0.95 to 0.99, the standard error of the mean will

a. double in size.

b. remain unchanged.

c. increase.

d. decrease.

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b

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the

a. margin of error.

b. proportion estimate.

c. same as α.

d. confidence coefficient.

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c

The margin of error in an interval estimate of the population mean is a function of all of the following except

a. variability of the population.

b. sample mean.

c. sample size.

d. α.

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b

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3 minutes. It is known that the standard deviation of the population of checkout times is 1 minute. The standard error of the mean equals

a. .010.

b. .100.

c. 1.000.

d. .001.

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b

The owners of an amusement park selected a random sample of 200 days and recorded the number of park patrons with annual passes who visited the park on each selected day. They computed a 90% confidence interval for the number of patrons with annual passes who visit the park daily. How would you interpret the 90% confidence interval of (35, 51)?

a. There is a 90% chance that the population mean number of patrons with annual passes who are in the park on any given day is between 35 and 51.

b. There is a 90% chance that the sample percentage of park patrons with annual passes is contained in the interval 35 to 51.

c. The method used to calculate the confidence interval has a 90% chance of producing an interval that captures the population mean number of annual pass holders in the park on any given day.

d. Ten percent of the population of annual pass holders visit the park on any given day.

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c

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3 minutes. It is known that the standard deviation of the population of checkout times is 1 minute. The 95% confidence interval for the true average checkout time (in minutes) is

a. 2.804 to 3.196.

b. 2.5 to 3.5.

c. 1 to 5.

d. 1.36 to 4.64.

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a

A random sample of 30 varieties of cereal was selected. The average number of calories per serving for these cereals is  = 120. Assuming that σ = 10, find a 95% confidence interval for the mean number of calories, μ, in a serving of cereal.

a. 116.42 to 123.58

b. 117.00 to 123.00

c. 118.00 to 122.00

d. 115.30 to 124.70

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a

Using α = 0.05, a confidence interval for a population proportion is determined to be 0.15 to 0.35. If the level of significance is increased, the interval for the population proportion

a. becomes narrower.

b. becomes wider.

c. does not change.

d. Not enough information is provided to answer this question.

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a

A random sample of 25 employees of a local company has been taken. A 95% confidence interval estimate for the mean systolic blood pressure for all employees of the company is 123 to 139. Which of the following statements is valid?

a. 95% of the sample of employees has a systolic blood pressure between 123 and 139.

b. If the sampling procedure were repeated many times, 95% of the sample means would be between 123 and 139.

c. 95% of the population of employees has a systolic blood pressure between 123 and 139.

d. If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

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d

The level of significance α

a. is (1 - confidence coefficient).

b. is always a negative value.

c. can be any positive value.

d. can be any value between -1.96 to 1.96.

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a

In an interval estimation for a proportion of a population, the value of z at 99.2% confidence is

a. 2.65.

b. 1.645.

c. 2.41.

d. 1.96.

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a

The use of the normal probability distribution as an approximation of the sampling distribution of p̄ is based on the condition that both np and n(1 - p) equal or exceed

a. 10.

b. 5.

c. 30.

d. .05.

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b

In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. With a .95 probability, the margin of error is approximately

a. 1.96.

b. .39.

c. 1.64.

d. .20.

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b

The value added to and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the

a. confidence level.

b. parameter estimate.

c. margin of error.

d. planning value.

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c

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3 minutes. It is known that the standard deviation of the population of checkout times is 1 minute. The 95% confidence interval for the true average checkout time (in minutes) is

a. 2.804 to 3.196.

b. 1.36 to 4.64.

c. 1 to 5.

d. 2.5 to 3.5.

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a

To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except

a. use the sample proportion from a preliminary sample.

b. use the sample proportion from a previous study.

c. use judgment or a best guess.

d. use 1.0 as an estimate.

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d

In order to estimate the average electric usage per month, a sample of 81 houses was selected and the electric usage was determined. Assume a population standard deviation of 450 kilowatt-hours. At 95% confidence, the size of the margin of error is

a. 50.00.

b. 98.00.

c. 1.96.

d. 42.00.

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b

The mean of the t distribution is

a. .5.

b. problem specific.

c. 1.

d. 0.

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d

The t distribution should be used whenever

a. the population is not normally distributed.

b. the sample size is less than 30.

c. the population standard deviation is known.

d. the sample standard deviation is used to estimate the population standard deviation.

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d

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the

a. margin of error.

b. confidence coefficient.

c. same as α.

d. proportion estimate.

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c

The general form of an interval estimate of a population mean or a population proportion is the _____ plus and minus the _____.

a. point estimate, margin of error

b. population proportion, standard error

c. population mean, standard error

d. planning value, confidence coefficient

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a

The level of significance α

a. can be any positive value.

b. is (1 - confidence coefficient).

c. is always a negative value.

d. can be any value between -1.96 to 1.96.

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b

In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. With a .95 probability, the margin of error is approximately

a. 1.64.

b. .39.

c. .20.

d. 1.96.

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b

In order to estimate the average electric usage per month, a sample of 81 houses was selected and the electric usage was determined. Assume a population standard deviation of 450 kilowatt-hours. If the sample mean is 1858 kWh, the 95% confidence interval estimate of the population mean is

a. 1758 to 1958 kWh.

b. 1760 to 1956 kWh.

c. 1776 to 1940 kWh.

d. 1729 to 1987 kWh.

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b

From a population with a variance of 900, a sample of 225 items is selected. At 95% confidence, the margin of error is

a. 15.

b. 3.92.

c. 4.

d. 2.0.

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b

The z value for a 97.8% confidence interval estimation is

a. 2.29.

b. 1.96.

c. 2.00.

d. 2.02.

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a

A machine that produces a major part for an airplane engine is monitored closely. In the past, 10% of the parts produced would be defective. With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is

a. 110.

b. 216.

c. 111.

d. 217.

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d

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3 minutes. It is known that the standard deviation of the population of checkout times is 1 minute. The standard error of the mean equals

a. .100.

b. 1.000.

c. .001.

d. .010.

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a

A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. If we want to provide a 95% confidence interval for the population mean SAT score, the degrees of freedom for reading the t value is

a. 63.

b. 60.

c. 61.

d. 62.

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a

A probability sampling method in which we randomly select one of the first k elements and then select every k th element thereafter is

a. cluster sampling.

b. systematic sampling.

c. convenience sampling.

d. stratified random sampling.

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b

The purpose of statistical inference is to provide information about the

a. population based upon information contained in the sample.

b. sample based upon information contained in the population.

c. mean of the sample based upon the mean of the population.

d. population based upon information contained in the population.

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a

All of the following are true about the standard error of the mean except

a. its value is influenced by the standard deviation of the population.

b. it is larger than the standard deviation of the population.

c. it decreases as the sample size increases.

d. it measures the variability in sample means.

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b

The sample mean is the point estimator of

a. p̄

b. x̄

c. σ

d. μ

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d

Random samples of size 36 are taken from an infinite population whose mean and standard deviation are 20 and 15, respectively. The distribution of the population is unknown. The mean and the standard error of the mean are

a. 20 and 15

b. 36 and 15

c. 20 and 2.5

d. 20 and 0.417

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c

A sample of 92 observations is taken from an infinite population. The sampling distribution of x̄ is approximately

a. normal because of the central limit theorem.

b. normal because the sample size is small in comparison to the population size.

c. normal because x̄ is always approximately normally distributed.

d. None of these alternatives are correct.

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a

For a population with any distribution, the form of the sampling distribution of the sample mean is

a. always normal for large sample sizes.

b. always normal for all sample sizes.

c. sometimes normal for all sample sizes.

d. sometimes normal for large sample sizes.

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a

A subset of a population selected to represent the population is

a. a small population.

b. a parameter.

c. a subset.

d. a sample.

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d

A subset of a population selected to represent the population is

a. a small population.

b. a parameter.

c. a subset.

d. a sample.

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d

A subset of a population selected to represent the population is

a. a small population.

b. a parameter.

c. a subset.

d. a sample.

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d

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3 minutes. It is known that the standard deviation of the population of checkout times is 1 minute. With a .95 probability, the sample mean will provide a margin of error of

a. .10.

b. .196.

c. 1.64.

d. 1.96.

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b

A random sample of 49 statistics examinations was taken. The average score, in the sample, was 84 with a variance of 12.25. The 95% confidence interval for the average examination score of the population of the examinations is

a. 77.40 to 86.60.

b. 80.48 to 87.52.

c. 82.99 to 85.01.

d. 68.00 to 100.00.

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c

A sample of 200 elements from a population with a known standard deviation is selected. For an interval estimation of μ, the proper distribution to use is the

a. normal distribution.

b. t distribution with 201 degrees of freedom.

c. t distribution with 199 degrees of freedom.

d. t distribution with 200 degrees of freedom.

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a

A sample of 200 elements from a population with a known standard deviation is selected. For an interval estimation of μ, the proper distribution to use is the

a. normal distribution.

b. t distribution with 201 degrees of freedom.

c. t distribution with 199 degrees of freedom.

d. t distribution with 200 degrees of freedom.

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a

A random sample of 25 employees of a local company has been taken. A 95% confidence interval estimate for the mean systolic blood pressure for all employees of the company is 123 to 139. Which of the following statements is valid?

a. If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

b. 95% of the sample of employees has a systolic blood pressure between 123 and 139.

c. 95% of the population of employees has a systolic blood pressure between 123 and 139.

d. If the sampling procedure were repeated many times, 95% of the sample means would be between 123 and 139.

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a

From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population (μ).

a. The sample size must be increased.

b. The normal distribution can be used.

c. The t distribution with 5 degrees of freedom must be used.

d. The t distribution with 6 degrees of freedom must be used.

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a

The t value for a 95% confidence interval estimation with 24 degrees of freedom is

a. 1.711.

b. 2.064.

c. 2.069.

d. 2.492.

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b

We are interested in conducting a study in order to determine the percentage of voters in a city who would vote for the incumbent mayor. What is the minimum sample size needed to estimate the population proportion with a margin of error not exceeding 4% at 95% confidence?

a. 601

b. 600

c. 626

d. 625

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a

The use of the normal probability distribution as an approximation of the sampling distribution of p̄ is based on the condition that both np and n(1 - p) equal or exceed

a. .05.

b. 10.

c. 30.

d. 5.

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d

It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is

a. 190.

b. 74.

c. 189.

d. 75.

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d

A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. The point estimate of the mean content of the bottles is

a. 0.02

b. 121

c. 0.22

d. 4

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d

The number of simple random samples of size 20 that can be selected from a finite population of size 25 is _____.

a. 20

b. 53,130

c. 1

d. 120

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b

The population we want to make inferences about is the

a. frame.

b. target population.

c. finite population.

d. sampled population.

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b

A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. The standard error of the mean equals

a. 0.0331

b. 0.3636

c. 0.0200

d. 4.000

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c

The following data was collected from a simple random sample of a population.

13

15

14

16

12

If the population consisted of 10 elements, how many different random samples of size 6 could be drawn from the population?

a. 362880

b. 60

c. 3024

d. 210

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d

Suppose candidate A for a town council seat receives 43% of the votes in an election. As voters leave the polls, they are asked who they voted for. What is the probability that less than 40% of the 80 voters surveyed indicate they voted for candidate A? Assume an infinite population.

a. .1368

b. .7061

c. .2939

d. .8632

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c

The probability distribution of all possible values of the sample mean x̄ is

a. the probability density function of x̄.

b. the grand mean, since it considers all possible values of the sample mean.

c. one, since it considers all possible values of the sample mean.

d. the sampling distribution of x̄.

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d

Parameters are

a. the averages taken from a sample.

b. numerical characteristics of either a sample or a population.

c. numerical characteristics of a population.

d. numerical characteristics of a sample.

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c

A probability distribution of all possible values of a sample statistic is known as

a. a sampling distribution.

b. a parameter.

c. simple random sampling.

d. a sample statistic.

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a

Suppose candidate A for a town council seat receives 43% of the votes in an election. As voters leave the polls, they are asked who they voted for. What is the probability that less than 40% of the 80 voters surveyed indicate they voted for candidate A? Assume an infinite population.

a. .8632

b. .2939

c. .1368

d. .7061

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b

How many different samples of size 3 can be taken from a finite population of size 10?

a. 30

b. 1,000

c. 720

d. 120

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d

As a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever

a. n ≥ 30 and (1 - p) = 0.5.

b. np ≥5, n ≥30.

c. np ≥5 and n(1-p) ≥5.

d. None of these alternatives are correct.

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c

In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. The probability that the sample proportion (the proportion living in the dormitories) is at least 0.30 is

a. 0.9328

b. 0.9664

c. 0.0336

d. 0.4664

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b

In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. The probability that the sample proportion (the proportion living in the dormitories) is at least 0.30 is

a. 0.9328

b. 0.9664

c. 0.0336

d. 0.4664

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b

The CEO of a large corporation is interested in the average salary of all managers for his large corporation. A sample of 500 managers found the average salary to be $56,500. Which of the following statements is correct?

a. The value $56,500 is a parameter.

b. The population size is 500 managers.

c. The average salary for all the managers will also be $56,500.

d. The average salary for the 500 managers can be used to estimate the average salary for all the managers.

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d

The proportion of students at a university who pass a biology class is p = .86. If 50 students are randomly selected, what is the probability that at least 75% of them have passed the class?

a. .9638

b. .9875

c. .0362

d. .0125

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b

Given the sampling distribution of the sample mean shown here, which of the following values is a reasonable estimate for the population mean?

a. 280

b. 300

c. .27

d. 320

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b

In point estimation

a. data from the sample is used to estimate the sample statistic.

b. the mean of the population equals the mean of the sample.

c. data from the sample is used to estimate the population parameter.

d. data from the population is used to estimate the population parameter.

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c

In point estimation

a. data from the sample is used to estimate the sample statistic.

b. the mean of the population equals the mean of the sample.

c. data from the sample is used to estimate the population parameter.

d. data from the population is used to estimate the population parameter.

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c

The sample mean is the point estimator of

a. μ

b. p̄

c. x̄

d. σ

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a

A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is

a. 0.7200

b. 8.3600

c. 0.0347

d. 0.9511

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d

When the selection of one element from the population influences the selection of another element, the sample

a. is from a finite population.

b. was selected using computer-generated random numbers.

c. contains selection bias.

d. is a simple random sample.

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c

The desired situation is when

a. the sampled population is larger than the targeted population.

b. the sampled population is smaller than the targeted population.

c. the sampled population is identical to the targeted population.

d. the sampled population is more varied than the targeted population.

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c

A sample of 25 observations is taken from an infinite population. The sampling distribution of p̄ is

a. not normal since n < 30

b. approximately normal because p̄ is always normally distributed

c. approximately normal if np > 30 and n(1-P) > 30

d. approximately normal if np ≥ 5 and n(1-P) ≥ 5

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d

Sampling distribution of x̄ is the

a. probability distribution of the sample proportion.

b. mean of the sample.

c. mean of the population.

d. probability distribution of the sample mean.

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d

Which of the following sampling methods does not lead to probability samples?

a. Stratified sampling

b. Cluster sampling

c. Systematic sampling

d. Convenience sampling

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d

A single numerical value used as an estimate of a population parameter is known as

a. a parameter.

b. a population parameter.

c. a mean estimator.

d. a point estimate.

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d

A single numerical value used as an estimate of a population parameter is known as

a. a parameter.

b. a population parameter.

c. a mean estimator.

d. a point estimate.

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d

A single numerical value used as an estimate of a population parameter is known as

a. a parameter.

b. a population parameter.

c. a mean estimator.

d. a point estimate.

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d

A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. The standard error of the mean is

a. 1.611.

b. .8083.

c. 7.0.

d. 80.83.

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b

Which of the following is not required when computing the sample size for an interval estimate of the population mean?

a. Population mean

b. Population standard deviation

c.

d. Margin of error the researcher is willing to accept

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a

We are interested in conducting a study in order to determine the percentage of voters in a city who would vote for the incumbent mayor. What is the minimum sample size needed to estimate the population proportion with a margin of error not exceeding 4% at 95% confidence?

a. 601

b. 600

c. 626

d. 625

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a

From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the

a. t distribution with 25 degrees of freedom.

b. normal distribution.

c. t distribution with 24 degrees of freedom.

d. t distribution with 26 degrees of freedom.

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c

A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is

a. 8.225.

b. 8.3.

c. 9.92.

d. 9.8.

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d

Using an α = .04, a confidence interval for a population proportion is determined to be .65 to .75. For the same data, if α is decreased, the confidence interval for the population proportion

a. uses a zero margin of error.

b. becomes narrower.

c. remains the same.

d. becomes wider.

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d

In order to estimate the average electric usage per month, a sample of 81 houses was selected and the electric usage was determined. Assume a population standard deviation of 450 kilowatt-hours. The standard error of the mean is

a. 450.

b. 500.

c. 81.

d. 50.

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d

In order to estimate the average electric usage per month, a sample of 81 houses was selected and the electric usage was determined. Assume a population standard deviation of 450 kilowatt-hours. The standard error of the mean is

a. 450.

b. 500.

c. 81.

d. 50.

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d

In order to estimate the average electric usage per month, a sample of 81 houses was selected and the electric usage was determined. Assume a population standard deviation of 450 kilowatt-hours. The standard error of the mean is

a. 450.

b. 500.

c. 81.

d. 50.

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d

In order to estimate the average electric usage per month, a sample of 81 houses was selected and the electric usage was determined. Assume a population standard deviation of 450 kilowatt-hours. The standard error of the mean is

a. 450.

b. 500.

c. 81.

d. 50.

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d

The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the

a. standard deviation.

b. sample size.

c. degrees of freedom.

d. finite correction factor.

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c

The degrees of freedom associated with a t distribution are a function of the

a. area in the upper tail.

b. sample standard deviation.

c. confidence coefficient.

d. sample size.

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d

From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population (μ).

a. The t distribution with 5 degrees of freedom must be used.

b. The normal distribution can be used.

c. The t distribution with 6 degrees of freedom must be used.

d. The sample size must be increased.

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d

The manager of a department store wants to determine the proportion of customers who use the store's credit card when making a purchase. What sample size should he select so that at 96% confidence the error will not be more than 10%?

a. 106

b. 76

c. 1

d. There is not enough information given to determine the sample size.

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a

Using an α = .04, a confidence interval for a population proportion is determined to be .65 to .75. For the same data, if α is decreased, the confidence interval for the population proportion

a. uses a zero margin of error.

b. becomes narrower.

c. becomes wider.

d. remains the same.

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c

A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is

a. 8.3.

b. 9.92.

c. 9.8.

d. 8.225.

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c

In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. With a .95 probability, the margin of error is approximately

a. 1.64.

b. 1.96.

c. .20.

d. .39.

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d

In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. With a .95 probability, the margin of error is approximately

a. 1.64.

b. 1.96.

c. .20.

d. .39.

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d

In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. With a .95 probability, the margin of error is approximately

a. 1.64.

b. 1.96.

c. .20.

d. .39.

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d

In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. With a .95 probability, the margin of error is approximately

a. 1.64.

b. 1.96.

c. .20.

d. .39.

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d

As the sample size increases, the margin of error

a. decreases.

b. stays the same.

c. increases.

d. fluctuates depending on the mean.

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a

When s is used to estimate σ, the margin of error is computed by using the

a. t distribution.

b. mean of the sample.

c. normal distribution.

d. mean of the population.

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a

What value of p should be used to compute the sample size that guarantees all estimates of proportions will meet the margin of error requirement?

a. 0.01

b. 0.25

c. 1

d. 0.50

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d

We can use the normal distribution to make confidence interval estimates for the population proportion, p, when

a. p has a normal distribution.

b. np ≥ 5.

c. both np ≥ 5 and n(1 - p) ≥ 5.

d. n(1 - p) ≥ 5.

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c

Which of the following must be decided by the researcher when computing the minimum sample size for an interval estimate of μ or p?

a. Mean

b. Standard deviation

c. Degrees of freedom

d. Margin of error

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d

The value added to and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the

a. parameter estimate.

b. confidence level.

c. margin of error.

d. planning value.

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c

The value added to and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the

a. parameter estimate.

b. confidence level.

c. margin of error.

d. planning value.

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c

The value added to and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the

a. parameter estimate.

b. confidence level.

c. margin of error.

d. planning value.

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c

The value added to and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the

a. parameter estimate.

b. confidence level.

c. margin of error.

d. planning value.

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c

The value added to and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the

a. parameter estimate.

b. confidence level.

c. margin of error.

d. planning value.

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c