Statistics Ch 1 to Ch 10 Quiz Questions and Answers

If the data distribution is symmetric, the skewness is

a. positive.

b. .5.

c. 0.

d. 1.

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c

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

a. 13.

b. 576.

c. 24.

d. 28,561.

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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. n1p1, n1(1 - p1), n2p2, n2(1 - p2)

b. n1p1, p1(1 - n1), n2p2, p2(1 - n2)

c. n1p2, n1(1 - p2), n2p1, n2(1 - p1)

d. n1p2, p2(1 - n2), n2p1, p1(1 - n1)

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a

The sample mean is the point estimator of

a. p̄

b. μ

c. x̄

d. σ

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b

In a random sample of 200 items, 5 items were defective. An estimate of the percentage of defective items in the population is

a. 5%.

b. 10%.

c. 2.5%.

d. 20%.

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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 mean, standard error

c. population proportion, standard error

d. planning value, confidence coefficient

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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. 70.00

b. 8.75

c. 27.78

d. 72.22

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c

When developing an interval estimate for the difference between two population means with sample sizes of n₁ and n₂,

a. n1 must be larger than n2.

b. n1 and n2 can be of different sizes.

c. n1 must be smaller than n2.

d. n1 must be equal to n2.

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b

Given that z is a standard normal random variable. What is the value of z if the area between -z and z is 0.754?

a. ± 1.16

b. ± 11.6

c. ± 1.96

d. ± 2.0

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a

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

a. statistical inference.

b. the sample.

c. descriptive statistics.

d. the population.

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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. 0.0668

b. 0.9332

c. 0.5668

d. 0.4332

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a

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. 0.0668

b. 0.9332

c. 0.5668

d. 0.4332

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a

Which of the following is not a scale of measurement?

a. Interval

b. Nominal

c. Ordinal

d. Primal

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d

The probability that a continuous random variable takes any specific value

a. is equal to zero.

b. is very close to 1.0.

c. depends on the probability density function.

d. is at least 0.5.

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a

Since a sample is a subset of the population, the sample mean

a. must be equal to the mean of the population.

b. varies around the mean of the population.

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

d. is always larger than the mean of the population.

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b

Since a sample is a subset of the population, the sample mean

a. must be equal to the mean of the population.

b. varies around the mean of the population.

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

d. is always larger than the mean of the population.

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b

x is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that x is greater than 10.52 is

a. 0.0838

b. 0.0029

c. 0.9971

d. 0.4971

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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. -1.740.

d. 2.12.

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a

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

a. 25.

b. 10.

c. 5.

d. 50.

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b

The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes. The probability that she will finish her trip in 80 minutes or less is

a. 0.02

b. 0.8

c. 1.00

d. 0.2

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b

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

The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable x to be the number of days Pete catches fish. The probability that Pete will catch fish on exactly one day is

a. .096

b. .104

c. .8

d. .008

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a

A simple random sample from an infinite population is a sample selected such that

a. each element has a probability of at least 0.5 of being selected.

b. each element has a 0.5 probability of being selected.

c. the probability of being selected changes.

d. each element is selected independently and from the same population.

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d

In a stem-and-leaf display,

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

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

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d

Positive values of covariance indicate

a. a positive variance of the x values.

b. the standard deviation is positive.

c. a positive variance of the y values.

d. positive relation between the independent and the dependent variables.

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d

The relative frequency of a class is computed by

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

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

c. dividing n by cumulative frequency of the class.

d. dividing the frequency of the class by n.

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d

Icon

Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the classical method for computing probability is used, the probability that the next customer will purchase a computer is

a. 0.75.

b. 1.00.

c. 0.25.

d. 0.50.

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c

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. normal distribution.

d. t distribution with 26 degrees of freedom.

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a

From nine cards numbered 1 through 9, two cards are drawn. Consider the selection and classification of the cards as odd or even as an experiment. How many sample points are there for this experiment?

a. 3

b. 9

c. 4

d. 2

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c

To compute the minimum sample size for an interval estimate of μ, we must first determine all of the following except

a. confidence level.

b. population standard deviation.

c. desired margin of error.

d. degrees of freedom.

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d

The range of probability is

a. minus infinity to plus infinity.

b. 0 to 1.

c. -1 to 1.

d. 0 to infinity.

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b

The probability of at least one head in two flips of a coin is

a. 0.33.

b. 0.25.

c. 0.50.

d. 0.75.

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d

Larger values of the standard deviation result in a normal curve that is

a. skewed to the left.

b. wider and flatter.

c. skewed to the right.

d. narrower and more peaked.

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b

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 70 degrees of freedom.

c. t distribution with 71 degrees of freedom.

d. t distribution with 73 degrees of freedom.

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b

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. independent samples.

c. conditional samples.

d. research samples.

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b

The degrees of freedom associated with a t distribution are a function of the

a. sample size.

b. confidence coefficient.

c. sample standard deviation.

d. area in the upper tail.

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

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

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

d. None of these alternatives are correct.

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b

x is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that x equals 19.62 is

a. 0.0055

b. 0.000

c. 0.9945

d. 0.4945

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b

The following data was collected from a simple random sample of a population.

13

15

14

16

12

The mean of the population

a. is 14

b. could be any value

c. is 15

d. is 15.1581

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b

A group of students had dinner at a local restaurant. The total bill for the dinner was $414.70. Each student paid his/her equal share of the bill, which was $18.85. How many student's were at the dinner?

a. 19

b. 22

c. 4

d. 415

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b

When the following hypotheses are being tested at a level of significance of α

H₀: μ ≥ 500
H_a: μ < 500

the null hypothesis will be rejected, if the p-value is

a. ≤ 1 - α/2.

b. > α.

c. = α/2.

d. ≤ α.

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d

For the standard normal probability distribution, the area to the right of the mean is

a. 3.09.

b. 0.5.

c. 1.

d. 1.96.

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b

iven that z is a standard normal random variable, what is the probability that -2.51 ≤ z ≤ -1.53?

a. 0.4950

b. 0.9310

c. 0.0570

d. 0.4370

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c

The critical value of t for a two-tailed test with 6 degrees of freedom using α = .05 is

a. 2.447.

b. 1.943.

c. 1.985.

d. 2.365.

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a

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. 0.1359

b. 0.3413

c. 0.8185

d. 0.4772

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a

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 4 customers and determining whether or not they purchase any merchandise. How many sample points exist in the above experiment? (Note that each customer is either a purchaser or non-purchaser.)

a. 16

b. 4

c. 2

d. 12

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a

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. Volume.

c. Variety.

d. Validity.

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d

If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is

a. 1/16.

b. larger than the probability of tails.

c. 1/2.

d. 0.

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c

If A and B are independent events with P(A) = .1 and P(B) = .4, then

a. P(A ∪ B) = .5.

b. P(A ∩ B) = 0.

c. P(A ∩ B) = .04.

d. P(A ∩ B) = .25.

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c

In statistical experiments, each time the experiment is repeated

a. the same outcome must occur.

b. a different outcome might occur.

c. the same outcome can not occur again.

d. a different out come must occur.

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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. .027.

b. .305.

c. .300.

d. .450.

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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. .0228.

b. .3.

c. less than .001.

d. more than .10.

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c

Facts and figures that are collected, analyzed and summarized for presentation and interpretation are

a. variables.

b. elements.

c. time series data.

d. data.

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d

The correlation coefficient ranges between

a. 1 and 100.

b. minus infinity and plus infinity.

c. -1 and +1.

d. 0 and 1.

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c

Which of the following is a scale of measurement?

a. Primal

b. Remedial

c. Divisional

d. Ratio

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d

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

a. the empirical rule.

b. a five number summary.

c. z-scores.

d. a histogram.

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b

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

An assumption made about the value of a population parameter is called a(n)

a. conclusion.

b. error.

c. hypothesis.

d. probability.

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c

The standard error of x̄₁ - x̄₂ is the

a. margin of error of x̄1 - x̄2.

b. standard deviation of the sampling distribution of x̄1 - x̄2.

c. pooled estimator of x̄1 - x̄2.

d. variance of the sampling distribution of x̄1 - x̄2.

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b

The probability distribution for the number of goals the Lions soccer team makes per game is given below.

Number Of Goals	Probability
0	0.05
1	0.15
2	0.35
3	0.30
4	0.15

What is the probability that in a given game the Lions do not score more than 2 goals?

a. 1.0

b. 0.95

c. 0.55

d. 0.20

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c

It is impossible to construct a frame for a(n)

a. infinite population.

b. finite population.

c. defined population.

d. target population.

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a

In a random sample of 100 observations, p̄ = .2. The 95.44% confidence interval for p is

a. .120 to .280.

b. .134 to .266.

c. .164 to .236.

d. .122 to .278.

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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. 1.328.

b. 2.528.

c. 1.325.

d. 2.539.

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a

As a general guideline, the research hypothesis should be stated as the

a. null hypothesis.

b. tentative hypothesis.

c. hypothesis the researcher wants to disprove.

d. alternative hypothesis.

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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 null hypothesis tested is H₀: μ_d = 0. The test statistic for the difference between the two population means is

a. 2.

b. -2.

c. -1.

d. 0.

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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 relative frequency for McDonalds?

a. .5

b. .4

c. .6

d. .27

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b

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

a. mode.

b. median.

c. outlier.

d. mean.

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a

The symbol ∩ shows the

a. intersection of two events.

b. sample space.

c. sum of the probabilities of events.

d. union of events.

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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 mean of the population is

a. 16

b. 19.6

c. 108

d. 18.0

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d

The expected value of a random variable is

a. the value of the random variable that occurs most frequently.

b. the value of the random variable that should be observed on the next repeat of the experiment.

c. the square root of the variance.

d. None of these alternatives are correct.

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d

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability the trip takes more than 20 minutes?

a. .6667

b. .3333

c. .1587

d. .8413

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d

If a six sided die is tossed two times and "3" shows up both times, the probability of "3" on the third trial is

a. much larger than any other outcome.

b. 1/216.

c. 1/6.

d. much smaller than any other outcome.

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c

The function that defines the probability distribution of a continuous random variable is a

a. probability density function.

b. uniform function.

c. normal function.

d. either normal of uniform depending on the situation.

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a

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 smaller than the mean of the population.

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

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

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

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c

z is a standard normal random variable. What is the value of z if the area between -z and z is 0.754?

a. 2.16

b. 0.377

c. 1.16

d. 0.123

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c

The uniform probability distribution is used with

a. any random variable, as long as it is not nominal.

b. a continuous random variable.

c. a normally distributed random variable.

d. a discrete random variable.

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b

A measure of the average value of a random variable is called a(n)

a. standard deviation.

b. expected value.

c. coefficient of variation.

d. variance.

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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 test statistic is

a. 1.96.

b. 1.65.

c. 2.00.

d. .05.

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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. -.92 to 6.92.

c. 0 to 6.92.

d. -1.96 to 1.96.

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b

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 3 customers and determining whether or not they purchase any merchandise. The number of sample points in this experiment is

a. 6.

b. 2.

c. 8.

d. 4.

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c

What is the mean of x, given the function below?

f(x) =(1/10) e^-x/10    x ≥ 0

a. 0.10

b. 10

c. 1,000

d. 100

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b

If P(A) = 0.7, P(B) = 0.6, P(A ∩ B) = 0, then events A and B are

a. non-mutually exclusive.

b. mutually exclusive.

c. complements of each other.

d. independent events.

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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. Let p_u represent the proportion under and p_o the proportion over the age of 18. The null hypothesis is

a. pu - po ≥ 0.

b. pu - po ≠ 0.

c. pu - po = 0.

d. pu - po ≤ 0.

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c

The sample size that guarantees the estimate of a population proportion satisfying the margin of error requirement is computed using a planning value of p equal to

a. .01.

b. .99.

c. .50.

d. .51.

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c

The p-value is a probability that measures the support (or lack of support) for

a. either the null or the alternative hypothesis.

b. neither the null nor the alternative hypothesis.

c. the null hypothesis.

d. the alternative hypothesis.

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c

The sample statistic s is the point estimator of

a. σ

b. μ

c. p̄

d. x̄

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a

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

a. σ2

b. μ

c. x̄

d. σ

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a

The key difference between the binomial and hypergeometric distribution is that, with the hypergeometric distribution

a. the trials are independent of each other.

b. the probability of success changes from trial to trial.

c. the random variable is continuous.

d. the probability of success must be less than 0.5.

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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. relative frequency distribution.

b. pie chart.

c. dot plot.

d. stem-and-leaf display.

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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

If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =

a. 0.59.

b. 0.43.

c. 0.75.

d. 0.14.

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b

A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is

a. at least one.

b. the same for each interval.

c. different for each interval.

d. zero.

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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. With a .95 probability, the sample mean will provide a margin of error of

a. 1.64.

b. .196.

c. 1.96.

d. .10.

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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. With a .95 probability, the sample mean will provide a margin of error of

a. 1.64.

b. .196.

c. 1.96.

d. .10.

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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 point estimate of the difference between the means of the two populations is

a. 4.

b. -28.

c. -4.

d. 3.

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d

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

a. n.

b. n + 1.

c. n - 1.

d. n - 2.

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a

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

a. n.

b. n + 1.

c. n - 1.

d. n - 2.

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a

The geometric mean of 1, 1, 8 is

a. 3.0.

b. 3.33.

c. 2.0.

d. 10.0.

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c

If two events are independent, then

a. the sum of their probabilities must be equal to one.

b. the product of their probabilities gives their intersection.

c. their intersection must be zero.

d. they must be mutually exclusive.

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b

Which of the following is a measure of variability?

a. Percentiles

b. Geometric mean

c. Interquartile range

d. Quartiles

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c

The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. What is the probability that a randomly selected tire will have a life of at least 47,500 miles?

a. 0.9332

b. 0.0668

c. 0.4993

d. 0.4332

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b

Geometric mean is a measure of

a. location.

b. variability.

c. dispersion.

d. weight.

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a

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

a. 35th percentile

b. Variance

c. Interquartile range

d. Standard deviation

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Solution

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b