Solutions Essentials of Modern Business Statistics with Microsoft Office Excel - 7th Edition - Chapter 12

12.1
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12.7 The following table contains observed frequencies for a sample of 200. Test for independence of the row and column variables using α = .05....
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12.8 The following table contains observed frequencies for a sample of 240. Test for independence of the row and column variables using α = .05....
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12.9 A Bloomberg Businessweek subscriber study asked, “In the past 12 months, when traveling for business, what type of airline ticket did you purchase most often?” A second question asked if the type of airline ticket purchased most often was for domestic or international travel. Sample data obtained are shown in the following table....
a. Using a .05 level of significance, is the type of ticket purchased independent of the type of flight? What is your conclusion?
b. Discuss any dependence that exists between the type of ticket and type of flight.

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12.10 A Deloitte employment survey asked a sample of human resource executives how their company planned to change its workforce over the next 12 months (INC. Magazine, February 2012). A categorical response variable showed three options: The company plans to hire and add to the number of employees, the company plans no change in the number of employees, or the company plans to lay off and reduce the number of employees. Another categorical variable indicated if the company was private or public. Sample data for 180 companies are summarized as follows....
a. Conduct a test of independence to determine if the employment plan for the next 12 months is independent of the type of company. At a .05 level of significance, what is your conclusion?
b. Discuss any differences in the employment plans for private and public companies over the next 12 months.

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12.11 Health insurance benefits vary by the size of the company (Atlanta Business chronicle, December 31, 2010). The sample data below show the number of companies providing health insurance for small, medium, and large companies. For purposes of this study, small companies are companies that have fewer than 100 employees. Medium-sized companies have 100 to 999 employees, and large companies have 1000 or more employees. The questionnaire sent to 225 employees asked whether or not the employee had company-sponsored health insurance and then asked the employee to indicate the size of the company....
a. Conduct a test of independence to determine whether company-sponsored health insurance coverage is independent of the size of the company. What is the p-value? Using a .05 level of significance, what is your conclusion?
b. A newspaper article indicated employees of small companies are more likely to lack company-sponsored health insurance coverage. Use percentages based on the above data to support this conclusion.

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12.12 A vehicle quality survey asked new owners a variety of questions about their recently purchased automobile (J.D. Power and Associates, March 2012). One question asked for the owner’s rating of the vehicle using categorical responses of average, outstanding, and exceptional. Another question asked for the owner’s education level with the categorical responses some high school, high school graduate, some college, and college graduate. Assume the sample data below are for 500 owners who had recently purchased an automobile....
a. Use a .05 level of significance and a test of independence to determine if a new owner’s vehicle quality rating is independent of the owner’s education. What is the p-value and what is your conclusion?
b. Use the overall percentage of average, outstanding, and exceptional ratings to comment upon how new owners rate the quality of their recently purchased automobiles.

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12.13 The Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the quality of management and the reputation of the company for over 250 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 following sample data for 200 respondents applies to this study....
a. Use a .05 level of significance and test for independence of the quality of management and the reputation of the company. What is the p-value and 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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12.16 On a syndicated television show the two hosts often create the impression that they strongly disagree about which movies are best. Each movie review is categorized as Pro (“thumbs up”), Con (“thumbs down”), or Mixed. The results of 160 movie ratings by the two hosts are shown here....Use a test of independence with a .01 level of significance to analyze the data. What is your conclusion?
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12.17 Use the sample data below to test the hypotheses...where pi is the population proportion of Yes responses for population i. Using a .05 level of significance, what is the p-value and what is your conclusion?...
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12.18
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12.19 The following sample data represent the number of late and on time flights for Delta, United, and US Airways (Bureau of Transportation Statistics, March 2012)....
a. Formulate the hypotheses for a test that will determine if the population proportion of late flights is the same for all three airlines.
b. Conduct the hypothesis test with a .05 level of significance. What is the p-value and what is your conclusion?
c. Compute the sample proportion of late flights for each airline. What is the overall proportion of late flights for the three airlines?

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12.20
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12.21 Kate Sanders, a researcher in the department of biology at IPFW University, studied the effect of agriculture contaminants on the fish population for streams in Northeastern Indiana (April 2012). 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....
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 .05 level of significance. What is the p-value and 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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12.22 A tax preparation firm is interested in comparing the quality of work at two of its regional offices. The observed frequencies showing the number of sampled returns with errors and the number of sampled returns that were correct are as follows....
a. What are the sample proportions of returns with errors at the two offices?
b. Use the chi-square test procedure to see if there is a significant difference between the population proportion of error rates for the two offices. Test the null hypothesis H0: p1 = p2 with a .10 level of significance. What is the p-value and what is your conclusion? Note:We generally use the chi-square test of equal proportions when there are three or more populations, but this example shows that the same chi-square test can be used for testing equal proportions with two populations.
c. In Section 11.1, a z test was used to conduct the above test. Either a χ2 test statistic or a z test statistic may be used to test the hypothesis. However, when we want to make inferences about the proportions for two populations, we generally prefer the z test statistic procedure. Refer to the Notes and Comments at the end of this section and comment on why the z test statistic provides the user with more options for inferences about the proportions of two populations.

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12.23
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12.24 A manufacturer is considering purchasing parts from three different suppliers. The parts received from the suppliers are classified as having a minor defect, having a major defect, or being good. Test results from samples of parts received from each of the three suppliers are shown below. Note that any test with these data is no longer a test of proportions for the three supplier populations because the categorical response variable has three outcomes: minor defect, major defect, and good....Using the data above, conduct a hypothesis test to determine if the distribution of defects is the same for the three suppliers. Use the chi-square test calculations as presented in this section with the exception that a table with r rows and c columns results in a chi-square test statistic with (r – 1)(c – 1) degrees of freedom. Using a .05 level of significance, what is the p-value and what is your conclusion?
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