Homework 4 (Chapter 11.1~11.4)
5. Americans spend an average of 8.6 minutes per day reading newspapers (U.S.A. Today, April 10, 1995). A researcher believes than individuals in management positions spend more than the national average time per day reading newspapers. A sample of individuals in management positions will be selected by the researcher. Data on newspaper-reading times will be used to test the following null and alternative hypotheses. .
a. What is the Type I error in this situation? What are the consequences of making this error?
b. What is the Type II error in this situation? What are the consequences of making this error?
10. Consider the following hypothesis test. . A sample size of 40 provides a sample mean of 16.5 and sample standard deviation of 7.
a. At , what is the critical value for , and what is the rejection rule?
b. Compute the value of the test statistic .
c. What is the p-value?
d. What is your conclusion?
12. Consider the following hypothesis test. . Assume the following test statistics. Compute the corresponding p-values and make the appropriate conclusions based on .
a. . b. . c. . d. . e. .
13. Individuals filing 1994 federal income tax returns prior to March 31, 1995, had an average refund of $1056 (U.S.A. Today, April 5, 1995). Consider the population of “last-minute” filers who mail their returns during the last five days of the income tax period (typically April 10 to April 15).
a. A researcher suggests that one of the reasons individuals wait until the last five days to file their returns is that on average those individuals have a lower refund than early filers. Develop appropriate hypotheses such that rejection of will support the researcher’s contention.
b. For a sample of 400 individuals who filed a return between April 10 and April 15, the sample mean refund was $910 and the sample standard deviation was $1600. At , what is your conclusion?
c. What is the p-value for the test?
15. (data set: Auto) According to the National Automobile Dealers Association, the mean price for used car is $10192 (U.S.A. Today, April 12, 1995). A manager of a Kansas City used car dealership selected a sample of 100 recent used car sales at the dealership. The sample data are contained in the data set Auto. Letting denote the population mean price for used cars at the Kansas City dealership, test
at a 0.05 level of significance.
a. What is the hypothesis-testing conclusion?
b. What is the p-value?
c. What information does the hypothesis test result provide for the manager of the Kansas City dealership? What follow-up action might the manager want to consider?
20 Consider the following hypothesis test. . A sample size of 50 provides a sample mean of 14.2 and sample standard deviation of 5.
a. At , what is the rejection rule?
b. Compute the value of the test statistic .
c. What is the p-value?
d. What is your conclusion?
21. Consider the following hypothesis test. . A sample size of 80 is used and the population standard deviation is 10. Use . Compute the value of the test statistic and specify your conclusion for each of the following sample results.
a. . b. . c. . d. .
22. Consider the following hypothesis test. . Assume the following test statistics. Compute the corresponding p-values and specify your conclusions based on .
a. . b. c. d. . e.
23. The Bureau of Economic Analysis in the U.S. Department of Commerce reported that the mean annual income for a resident of North Carolina is $18688 (U.S.A. Today, August 24, 1995). A researcher for the state of South Carolina wants to test , to see if the mean annual income for a resident of South Carolina is different.
a. What is the appropriate conclusion if a sample of 400 residents of South Carolina shows a sample mean annual income of $16860 and a sample standard deviation of $14624? Use a 0.05 level of significance.
b. What is the p-value for this test.
28. The mean salary for full professors in the United States is $61650 (The American Almanac of Jobs and Salaries, 1994-1995 Edition). A sample of 36 full professors at business colleges showed and .
a. Develop a 95% confidence interval for the population mean salary of business college professors.
b. Use the confidence interval to conduct the hypothesis test: . What is your conclusion?
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