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Consider
the following hypothesis test. : : Excel
File: data10-03.xlsx
Enter
negative values as negative numbers. a. What is the value of the test statistic? (to 2 decimals) b. What is the -value? (to 4 decimals) c. With , what is your hypothesis testing conclusion?
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Consumer
Reports uses a survey of readers to
obtain customer satisfaction ratings for the nation's largest supermarkets (Consumer
Reports website). Each survey respondent is asked to rate a
specified supermarket based on a variety of factors such as quality of
products, selection, value, checkout efficiency, service, and store layout.
An overall satisfaction score summarizes the rating for each respondent
with meaning the respondent is completely satisfied in terms of
all factors. Sample data representative of independent samples of Publix and
Trader Joe's customers are shown below. Excel
File: data10-07.xlsx
a. Formulate the null and alternative hypotheses to test whether there is
a difference between the population mean customer satisfaction scores for the
two retailers. b. Assume that experience with the Consumer Reports satisfaction
rating scale indicates that a population standard deviation of is
a reasonable assumption for both retailers. Conduct the hypothesis test and
report the -value. -value
= (to decimals) At
a level of significance what is your conclusion?
I.
Reject . There is not sufficient
evidence to conclude that the mean satisfaction scores differ for the two
retailers.
II.
Do not reject . There is not
sufficient evidence to conclude that the mean satisfaction scores differ for
the two retailers.
III.
Reject . There is sufficient
evidence to conclude that the mean satisfaction scores differ for the two
retailers.
IV.
Do not reject . There is
sufficient evidence to conclude that the mean satisfaction scores differ for
the two retailers. c. Which retailer, if either, appears to have the greater customer satisfaction? Provide
a confidence interval for the difference between the population
mean customer satisfaction scores for the two retailers. Enter negative
values as negative numbers, if any. to (to decimals)
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Consider
the following data for two independent random samples taken from two normal
populations.
a. Compute the two sample means. (to nearest whole number) b. Compute the two sample standard deviations. (to 2 decimals) c. What is the point estimate of the difference between the two
population means? d. What is the confidence interval estimate of the
difference between the two population means? (to 2 decimals and enter
negative value as negative number)
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The
increasing annual cost (including tuition, room, board, books and fees) to
attend college ) to attend college has been widely discussed in many
publications including Money magazine. The following random
samples show the annual cost of attending private and public colleges. Data
are in thousands of dollars. Click on the datafile logo to reference the
data. Round degrees of freedom to the preceding whole number.
a. Compute the sample mean and sample standard deviation for private and
public colleges. Round your answers to two decimal places. = = = = b. What is the point estimate of the difference between the two
population means? Round your answer to one decimal place. Interpret
this value in terms of the annual cost of attending private and public
colleges. c. Develop a confidence interval of the difference between the
mean annual cost of attending private and public colleges. confidence
interval, private colleges have a population mean annual cost to more expensive than public colleges.
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Periodically,
Merrill Lynch customers are asked to evaluate Merrill Lynch financial
consultants and services. Higher ratings on the client satisfaction survey
indicate better service with the maximum service rating.
Independent samples of service ratings for two financial consultants are
summarized here. Consultant A has years of experience, whereas
consultant B has year of experience. Use and test to
see whether the consultant with more experience has the higher population
mean service rating. Round degrees of freedom to previous whole number. Excel
File: data10-17.xlsx
a. State the null and alternative hypotheses. b. Compute the value of the test statistic. (to 2 decimals) c. What is the p-value? Use Table 2 from Appendix B to find the values that bound the test statistic. d. What is your conclusion?
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Bank
of America's Consumer Spending Survey collected data on annual credit card
charges in seven different categories of expenditures: transportation,
groceries, dining out, household expenses, home furnishings, apparel, and
entertainment. Using data from a sample of credit card accounts,
assume that each account was used to identify the annual credit card charges
for groceries (population 1) and the annual credit card charges for dining
out (population 2). Using the difference data, the sample mean difference
was , and the sample standard deviation was . a. Formulate the null and alternative hypotheses to test for no
difference between the population mean credit card charges for groceries and
the population mean credit card charges for dining out. b. Use level of significance. Can you conclude that the
population means differ? What
is the -value? (to 6 decimals) c. Which category, groceries or dining out, has a higher population
mean annual credit card charge? What
is the point estimate of the difference between the population means? Round
to the nearest whole number. What
is the confidence interval estimate of the difference between the
population means? Round to the nearest whole number.
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The
College Board SAT college entrance exam consists of two sections: math and
evidence-based reading and writing (EBRW). Sample data showing the math and
EBRW scores for a sample of students who took the SAT follow.
Click on the datafile logo to reference the data.
a. Use a level of significance and test for a difference
between the population mean for the math scores and the population mean for
the EBRW scores. What
is the test statistic? Enter negative values as negative numbers. Round your
answer to two decimal places. What
is the -value? Round your answer to four decimal places. What
is your conclusion?
I.
Reject . We cannot conclude that
there is a significant difference between the population mean scores for the
SAT math test and the SAT writing test.
II.
Do not reject . We cannot
conclude that there is a significant difference between the population mean
scores for the SAT math test and the SAT writing test.
III.
Reject . We can conclude that
there is a significant difference between the population mean scores for the
SAT math test and the SAT writing test.
IV.
Do not reject . We can conclude
that there is a significant difference between the population mean scores for
the SAT math test and the SAT writing test. b. What is the point estimate of the difference between the mean scores
for the two tests? What
are the estimates of the population mean scores for the two tests?
Which
test reports the higher mean score?
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A
personal fitness produces both a deluxe and a standard model of a smoothie
blender for home use. Selling prices obtained from a sample of retail outlets
follow. Excel
File: data10-27.xlsx
Round
your answers to 2 decimal places. a. The manufacturer's suggested retail prices for the two models show
a price differential. Use a level of significance and
test that the mean difference between the prices of the two models
is . b. What is the confidence interval for the difference between
the mean prices of the two models? to
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Consider
the hypothesis test below. The
following results are for independent samples taken from the two populations.
a. What is the -value (to 4 decimals)? Use Table 1 from Appendix B. b. With , what is your hypothesis testing conclusion?
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Tourism
is extremely important to the economy of Florida. Hotel occupancy is an
often-reported measure of visitor volume and visitor activity (Orlando
Sentinel, May , ). Hotel occupancy data for February in two
consecutive years are as follows.
a. Formulate the hypothesis test that can be used to determine
whether there has been an increase in the proportion of rooms occupied over
the one-year period.
b. What is the estimated proportion of hotel rooms occupied each
year (to decimals)?
c. Conduct a hypothesis test. What is the -value
(to decimals)? Use Table 1 from Appendix B. -value
= Using
a level of significance, what is your conclusion? We that
there has been an increase in the hotel occupancy rate. d. What is the confidence interval estimate of the
change in occupancy for the one-year period (to decimals)? to Do
you think area officials would be pleased with the results? Officials
would likely be with
the occupancy statistics as the trend for the current year is in
hotel occupancy rates compared to last year.
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The
National Association of Home Builders provided data on the cost of the most
popular home remodeling projects. Sample data on cost in thousands of dollars
for two types of remodeling projects are as follows. Excel
File: data10-41.xlsx
a. Develop a point estimate of the difference between the
population mean remodeling costs of kitchens and master bedrooms. (Enter
negative values as negative numbers. Report in thousands of dollars with no
commas in your answer.) b. Develop a confidence interval for the difference
between the two population means. (to 1 decimal and enter negative values as
negative numbers)
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Country
Financial, a financial services company, uses surveys of adults
age and older to determine whether personal financial fitness is
changing over time. A recent sample of adults
showed indicating that their financial security was more than
fair. Just a year prior, a sample of adults
showed indicating that their financial security was more than
fair. a. State the hypotheses that can be used to test for a significant
difference between the population proportions for the two years. b. Conduct the hypothesis test and compute the -value. Round your
answer to four decimal places. At level
of significance, what is your conclusion?
I.
Reject . There is not sufficient
evidence to conclude that the population proportions are not equal. The data
do not suggest that there has been a change in the population proportion
saying that their financial security is more than fair.
II.
Reject . There is sufficient
evidence to conclude that the population proportions are not equal. The data
suggest that there has been a change in the population proportion saying that
their financial security is more than fair.
III.
Do not reject . There is not
sufficient evidence to conclude that the population proportions are not
equal. The data do not suggest that there has been a change in the population
proportion saying that their financial security is more than fair.
IV.
Do not reject . There is
sufficient evidence to conclude that the population proportions are not
equal. The data suggest that there has been a change in the population
proportion saying that their financial security is more than fair. c. What is the confidence interval estimate of the difference
between the two population proportions? Round your answers to four decimal
places.
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Each
year, over million people in the United States become infected
with bacteria that are resistant to antibiotics. In particular, the Centers
of Disease Control and Prevention has launched studies of drug-resistant
gonorrhea (CDC.gov website). Of cases tested in
Alabama, were found to be drug-resistant. Of cases
tested in Texas, were found to be drug-resistant. Do these data
suggest a statistically significant difference between the proportions of
drug-resistant cases in the two states? Use a level of
significance. What is the -value, and what is your conclusion? Test
statistic = (to 2 decimals) -value
= (to 4 decimals) Conclusion: Choose
the correct option. There
is a significant difference in drug resistance between the two states.
Alabama has the higher drug resistance rate.
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|
Find
the following chi-square distribution values from Table 11.1 or Table 3 of Appendix B. (to decimals) a. with b. with c. with d. with e. with
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|
In ,
Mike Krzyewski and John Calipari topped the list of highest paid college
basketball coaches (Sports Illustrated website). The following
sample shows the head basketball coach's salary for a sample of schools
playing NCAA Division I basketball. Salary data are in millions of dollars. Excel
File: data11-05.xlsx
a. Use the sample mean for the schools to estimate the
population mean annual salary for head basketball coaches at colleges and
universities playing NCAA Division I basketball (to decimals). $ million b. Use the data to estimate the population standard deviation for the
annual salary for head basketball coaches (to decimals). $ million c. What is the confidence interval for the population variance
(to decimals)? Use Table 11.1. ($ million, $ million) d. What is the confidence interval for the population standard
deviation (to decimals)? Use Table 11.1. ($ million, $ million)
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In ,
Americans spent a record-high billion on Halloween-related
purchases (the balance website). Sample data showing the
amount, in dollars, adults spent on a Halloween costume are as
follows.
a. What is the estimate of the population mean amount adults spend
on a Halloween costume (to decimals)? b. What is the sample standard deviation (to decimals)? c. Provide a confidence interval estimate of the
population standard deviation for the amount adults spend on a Halloween
costume (to decimals). Use Table 11.1.
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The
competitive advantage of some small American factories such as In Tolerance
Contract Manufacturing lies in their ability to produce parts with very
narrow requirements, or tolerances, that are typical in the aerospace
industry. Consider a product with specifications that call for a maximum
variance in the lengths of the parts of . Suppose the sample variance
for parts turns out to be . Use , to test whether the
population variance specification is being violated. : Test
statistic = (to 2 decimals, if required) The -value
is .
Use Table 11.1.
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|
Find
the following distribution values from Table 4 of Appendix B (available online). a. with degrees of freedom and b. with degrees of freedom and c. with degrees of freedom and d. with degrees of freedom and
|
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|
In
its Auto Reliability Survey, Consumer Reports asked
subscribers to report their maintenance and repair costs. Most individuals
are aware of the fact that the average annual repair cost for an automobile
depends on the age of the automobile. A researcher is interested in finding
out whether the variance of the annual repair costs also increases with the
age of the automobile. A sample of automobiles years
old showed a sample standard deviation for annual repair costs
of and a sample of automobiles years old
showed a sample standard deviation for annual repair costs of . a. State the null and alternative versions of the research
hypothesis that the variance in annual repair costs is larger for the older
automobiles. Let year old automobiles be represented by
population . b. At a level of significance, what is your conclusion? Calculate
the value of the test statistic (to decimals). The -value
is .
Use Table 4 of Appendix B. that year
old automobiles have a larger variance in annual repair costs compared
to year old automobiles.
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The
variance in a production process is an important measure of the quality of
the process. A large variance often signals an opportunity for improvement in
the process by finding ways to reduce the process variance. Jelly Belly Candy
Company is testing two machines that use different technologies to fill three
pound bags of jelly beans. The file Bags contains a sample
of data on the weights of bags (in pounds) filled by each machine.Conduct a
statistical test to determine whether there is a significant difference
between the variances in the bag weights for the two machines. Use
a level of significance. What is your conclusion? Which machine,
if either, provides the greater opportunity for quality improvements? Click
on the datafile logo to reference the data.
(to decimals) (to decimals) (to decimals)
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Battery
life is an important issue for many smartphone owners. Public health studies
have examined "low-battery anxiety" and acute anxiety called
"nomophobia" that results when a smartphone user's phone battery
charge runs low and then dies (Wall Street Journal, May , ).
Battery life between charges for the Samsung Galaxy S9
averages hours when the primary use is talk time
and hours when the primary use is Internet applications. Because
the mean hours for talk time usage is greater than the mean hours for
Internet usage, the question was raised as to whether the variance in hours of
usage is also greater when the primary use is talk time. Sample data showing
battery life between charges for the two applications follows. Click on the
datafile logo to reference the data.
a. Formulate hypotheses about the two population variances that can be
used to determine whether the population variance in battery life is greater
for the talk time application. Consider the talk time use as
population and Internet use as population . b. What are the standard deviations of battery life for the two
samples (to decimals)? c. Conduct the hypothesis test and compute the -value. -value
= (to decimals) Using
a level of significance, what is your conclusion? .
We that
the population variance in battery hours of use for the talk time application
is larger than the population variance in battery hours of use for the
Internet application.
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Because
of staffing decisions, managers of the Gibson-Marimont Hotel are interested
in the variability in the number of rooms occupied per day during a
particular season of the year. A sample of days of operation shows
a sample mean of rooms occupied per day and a sample standard
deviation of rooms. a. What is the point estimate of the population variance (to
nearest whole number)? b. Provide a confidence interval estimate of the
population variance (to nearest whole number). Use Table 11.1. ( , ) c. Provide a confidence interval estimate of the
population standard deviation (to decimal). Use Table 11.1. ( , )
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According
to the Corporate Travel Index compiled by Business Travel
News, the average daily cost for business travel in the United States
rose to per day (Executive Travel website). The
file Travel contains sample data for an analogous study on
the estimated daily living costs for an executive traveling to various
international cities. The estimates include a single room at a four-star
hotel, beverages, breakfast, taxi fares, and incidental costs. Click on the
datafile logo to reference the data.
a. Compute the sample mean (to decimals). b. Compute the sample standard deviation (to decimals). c. Compute a confidence interval for the population
standard deviation (to decimals). Use Table 11.1.
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Filling
boxes with consistent amounts of its cereals are critical to General Mills’
success. The filling variance for boxes of Count Chocula cereal is designed
to be ounces2 or less. A sample
of boxes of Count Chocula shows a sample standard deviation
of ounces. Use to determine whether the variance in the
cereal box fillings is exceeding the design specification. Use Table 11.1. Test
statistic = (to decimals) Interpret:
The population variance appears to be exceeding the standard.
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A
sample of days over the past six months showed that that Philip
Sherman, DDS, treated the following numbers of
patients: , , , , , , , , and .
If the number of patients seen per day is normally distributed, would an
analysis of these sample data reject the hypothesis that the variance in the
number of patients seen per day is equal to ? Use level of
significance. Use Table 3 from Appendix B. State
the hypotheses. : 10 : 10 Calculate
the variance and test statistic. (to 2 decimals) variance
= test
statistic = What
is your conclusion?
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Stable
cost reporting in a manufacturing setting is typically a sign that operations
are running smoothly. The accounting department at Rockwell Collins, an
avionics manufacturer, analyzes the variance of the weekly costs reported by
two of its production departments. A sample of cost reports for
each of the two departments shows cost variances of and ,
respectively. Is this sample sufficient to conclude that the two production
departments differ in terms of unit cost variance?
Use (to decimals). Test
statistic =
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During
the first weeks of the television season, the Saturday evening
8:00 P.M. to
9:00 P.M. audience
proportions were recorded as ABC , CBS , NBC , and Independents .
A sample of homes two weeks after a Saturday night schedule
revision yielded the following viewing audience data: ABC homes,
CBS homes, NBC homes, and
Independents homes. Test with to determine whether the
viewing audience proportions changed. Find
the test statistic and p-value. (Round your test statistic to two
decimal places. Use Table 3 of Appendix B.) Test
statistic = -value
is . Conclusion:
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The
following table contains observed frequencies for a sample of .
Test
for independence of the row and column variables using . Compute
the value of the test statistic (to 2 decimals). Use
Table 3 of Appendix B to find the -value. The -value
is What
is your conclusion?
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In ,
Addison Group and Kelton surveyed the work preferences and attitudes
of working adults spread over three generations — Baby Boomers,
Generation X, and Millennials (Society for Human Resource Management website).
One question asked individuals if they would leave their current job to make
more money at another job. The file Millennials contains the
sample data, which is also summarized in the following table. Click
on the datafile logo to reference the data.
Conduct
a test of independence to determine whether interest in leaving a current job
for more money is independent of employee generation. Compute
the value of the test statistic (to decimals). Do not
round your intermediate calculation. What
is the -value? Use Table 3 of Appendix B. The -value
is . Using
a level of significance, what is your conclusion? Conclude
interest in leaving job for more money independent
of the employee generation.
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The
Wall Street Journal Corporate Perceptions Study
surveys readers and asks how each rats the quality of management and the
reputation of the company for over worldwide corporations. Both
the quality of management and the reputation of the company were rated on an
excellent, good, and fair categorical scale. Assume the sample data
for respondents below applies to this study.
a. Use level of significance and test for independence of the
quality of management and the reputation of the company. Compute
the value of the test statistic (to 2 decimals). Do not round
intermediate calculations. Use
Table 3 of Appendix B to find the -value. The -value
is What
is your conclusion? b. If there is a dependence or association between the two ratings,
discuss and use probabilities to justify your answer.
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Use
the sample data below to test the hypotheses
where is
the population proportion of Yes responses for population .
Using
a level of significance, what is the -value? Use Table 3
of Appendix B. The -value
is What
is your conclusion?
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The
following sample data represent the number of late and on time flights for
the Delta, United and US Airways. Excel
File: data12-19.xlsx
a. Formulate the hypotheses for a test that will determine whether the
population proportion of late flights is the same for all three airlines. b. Conduct the hypothesis test with a level of significance.
What is the -value? Use Table 3 of Appendix B. The p-value
is What
is your conclusion? c. Compute the sample proportion of late flights for each airline. (to 2 decimals) (to 2 decimals) (to 2 decimals) What
is the overall proportion of late flights for the three airlines? Round your
answer to three decimal places. The
overall proportion of late flights for the three airlines is
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Kate
Sanders, a researcher in the department of biology at IPFW University,
studied the effect of agriculture contaminants on the stream fish population
in northeastern Indiana. Specially designed traps collected samples of fish
at each of four stream locations. A research question was, Did the
differences in agricultural contaminants found at the four locations alter
the proportion of the fish population by gender? Observed frequencies were as
follows. Excel
File: data12-21.xlsx
a. Focusing on the proportion of male fish at each location, test the
hypothesis that the population proportions are equal for all four locations.
Use a level of significance. 1. 2. 3. Choose
correct answer from above choice : What
is the -value? Use Table 3 of Appendix B. The -value
is What
is your conclusion? b. Does it appear that differences in agricultural contaminants found at
the four locations altered the fish population by gender?
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Social
media is popular around the world. Statista provides estimate of the number
of social media users in various countries in as well as the
projections for . Assume that the results for surveys in the United
Kingdom, China, Russia, and the United States are as follows. Excel
File: data12-23.xlsx
a. Conduct a hypothesis test to determine whether the proportion of
adults using social media is equal for all four countries. Using
a level of significance. 1. 2. 3. Choose
correct answer from above choice H a: What
is the -value? Use Table 3 of Appendix B. The -value
is What
is your conclusion? Conclude
the all population proportions are . b. What are the sample proportions for each of the four countries? Round
your answers to two decimal places.
Which
country has the largest proportion of adults using social networking sites? c. Using a level of significance, conduct multiple pairwise
comparison tests among the four countries.
Round , and to two decimal places.
Round to four decimal places.
What
is your conclusion? Only
two comparisons are not significant .
All other comparisons show a significant difference.
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Historically,
the industries with the most complaints to the Better Business Bureau have
been banks, cable and satellite television companies, collection agencies,
cellular phone providers, and new car dealerships. The results for a sample
of complaints are contained in the file BBB. Click on
the datafile logo to reference the data.
a. Construct a frequency distribution for the number of complaints by
industry.
b. Using , conduct a hypothesis test to determine whether the
probability of a complaint is the same for the five industries. The
test-statistic is (to 3 decimals). -value (to 4 decimals) What
is your conclusion? c. Which industry has the most complaints? Dropping
the industry with the most complaints using , conduct a hypothesis test
to determine whether the probability of a complaint is the same for the
remaining four industries. The
test-statistic is (to 3 decimals). -value (to 4 decimals) What
is your conclusion?
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Based
on sales, the six top-selling compact cars are the Honda Civic,
Toyota Corolla, Nissan Sentra, Hyundai Elantra, Chevrolet Cruze, and Ford
Focus (New York Daily News). The market shares are Honda
Civic , Toyota Corolla , Nissan Sentra , Hyundai
Elantra , Chevrolet Cruze , and Ford Focus , with other small
car models comprising the remaining . A sample of compact car
sales in Chicago showed the following number of vehicles sold. Excel
File: data12-27.xlsx
Use
a goodness of fit test to determine whether the sample data indicate that the
market shares for cars in Chicago are different than the market shares
suggested by nationwide sales. Using a level of
significance, what is the -value? Use Table 3 of Appendix B. The -value
is . What
is your conclusion? Conclude
that the markets shares for the seven compact cars in Chicago the
market shares reported. What
market share differences, if any, exist in Chicago? Round your answers to
three decimal places. Enter negative values as negative numbers.
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Bara
Research Group conducted a survey about church attendance. The survey
respondents were asked about their church attendance and asked to indicate
their age. Use the sample data to determine whether church attendance is
independent of age. Using a level of significance, what is
the -value? Excel
File: data12-29.xlsx
Use
Table 3 of Appendix B to find the -value. The -value
is . What
is your conclusion? Conclude
church attendance is of
age. What
conclusion can you draw about church attendance, as individuals grow older? Church
attendance as
individuals grow older.
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In
a study, Phoenix Marketing International identified Bridgeport,
Connecticut; San Jose, California; Washington, DC; and Lexington Park,
Maryland, as the four U.S. cities with the highest percentage of millionaires
(Kiplinger website). Consider a sample of data that show the
following number of millionaires for samples of individuals from each of the
four cities.
a. What is the estimate of the percentage of millionaires in each
of these cities (to 1 decimal)?
b. Using level of significance, test for the equality of
the population proportion of millionaires for these four cities. What is the -value? Compute
the value of the test statistic (to 3 decimals). Use
Table 3 of Appendix B to find the -value. The -value
is What
is your conclusion? that
there is a difference among the population proportion of millionaires for
these four cities.
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Is
there any difference in the variability in golf scores for players on the
LPGA Tour (the women's professional golf tour) and players on the PGA Tour
(the men's professional golf tour)? A sample of tournament scores
from LPGA events showed a standard deviation of strokes, and a
sample of tournament scores from PGA events showed a standard
deviation of . Conduct a hypothesis test for equal population variances
to determine whether there is any statistically significant difference in the
variability of golf scores for male and female professional golfers. Use . What
is your conclusion? There
is significant
difference in the variances.
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