# Homework 5 (Chapter 11

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Homework 5 (Chapter 11.5~12.2)

Chapter 11.5~11.6

29. Consider the following hypothesis test, [pic]. A sample of 16 provides a sample mean of 11 and sample standard deviation of 3.

a. With [pic], what is the rejection rule?

b. Compute the value of the test statistic [pic]. What is your conclusion?

30. Consider the following hypothesis test, [pic]. Data from a sample of six items are: 18, 20, 16, 19, 17, 18.

a. Compute the sample mean.

b. Compute the sample standard deviation.

c. With [pic], what is the rejection rule?

d. Compute the value of the test statistic [pic].

32. Consider the following hypothesis test, [pic]. Assume a sample of 16 items provides the following test statistics. What can you say about the p-values in each case? What are your conclusions based on [pic]?

a. [pic] b. [pic]. c. [pic]. d. [pic] e. [pic]

35. On the average, a housewife with a husband and two children is estimated to work 55 hours or less per week on household-related activities. The hours worked during a week for a sample of eight housewives are: 58, 52, 64, 63, 59, 62, 62, and 55.

a. Use [pic] to test [pic]. What is your conclusion about the mean number of hours worked per week?

b. What can you say about the p-value?

40. Consider the following hypothesis test, [pic]. A sample of 400 provided a sample proportion of [pic].

a. At [pic], what is the rejection rule?

b. Compute the value of the test statistic [pic].

c. What is the p-value?

41. Consider the following hypothesis test, [pic]. A sample of 300 is selected. Use [pic]. Provide the value of the test statistic [pic], the p-values, and your conclusion for each of the following sample results.

a. [pic]. b. [pic]. c. [pic]. d. [pic].

45. (data set: Students) A magazine claims that 25% of its readers are college students. A random sample of 200 readers resulted in the data set Students. A response of Yes indicates that the reader is a college student. Use a 0.10 level of significance to test [pic]. What is the p-value?

49. At least 20% of all workers are believed to be willing to work fewer hours for less pay to obtain more time for personal and leisure activities. A USA Today/CNN/Gallup poll with a sample of 596 respondents found 83 willing to work fewer hours for less pay to obtain more personal and leisure time (USA Today, April 10, 1995). Test [pic] using a 0.05 level of significance. What is your conclusion?

Chapter 12.1~12.2

1. Consider the following results for two independent random samples taken from two populations.

|Sample 1 |Sample 2 |

|[pic] |[pic] |

|[pic] |[pic] |

|[pic]s |[pic] |

a. What is the point estimate of the difference between the two population means?

b. Provide a 90% confidence interval for the difference between the two population means.

c. Provide a 95% confidence interval for the difference between the two population means.

3. Consider the following data for two independent random samples taken from two

populations.

|Sample 1 |Sample 2 |

|10, 12, 7, 7, 7, 9 |8, 8, 6, 7, 4, 9 |

a. Compute the two sample means.

b. Compute the two sample standard deviations.

c. What is the point estimate of the difference between the two population means?

d. What is the pooled estimate of the population variance?

e. Develop a 95% confidence interval for the difference between the two population means.

9. Women who are union members earn \$2.50 per hour more than women who are not union members (The Wall Street Journal, July 26, 1994). Suppose independent random samples of 15 unionized women and 20 nonunionized women in manufacturing have been selected and the following hourly wage rates are found.

|Union Workers |Nonunion Workers |

|22.4, 18.9, 16.7, 14.05, 16.20, 20, 16.1, 16.3, 19.1, 16.5, |17.6, 14.4, 16.6, 15, 17.65, 15, 17.55, 13.3, 11.2, 15.9, |

|18.5, 19.8, 17, 14.3, 17.2 |19.2, 11.85, 16.65, 15.2, 15.3, 17, 15.1, 14.3, 13.9, 14.5 |

a. Suppose we want to develop an interval estimate of the difference in the mean wage rates between unionized and nonunionized women working in manufacturing. What assumptions must be made about the two populations?

b. What is the pooled estimate of the population variance?

c. Develop a 95% confidence interval for the difference between the two population means.

d. Does there appear to be any difference in the mean wage rate between these two groups? Explain.

10. Consider the following hypothesis test, [pic]. The following results are for two independent samples taken from the two populations.

|Sample 1 |Sample 2 |

|[pic] |[pic] |

|[pic] |[pic] |

|[pic] |[pic] |

a. With [pic], what is your hypothesis-testing conclusion?

b. What is the p-value?

12. Consider the following hypothesis test, [pic]. The following results are for two independent samples taken from the two populations. With [pic], what is your hypothesis-testing conclusion?

|Sample 1 |Sample 2 |

|[pic] |[pic] |

|[pic] |[pic] |

|[pic] |[pic] |

17. Starting annual salaries for individuals entering the public accounting and financial planning professions were presented in Fortune, June 26, 1995. The Starting salaries for a sample of 12 public accountants and a sample of 14 financial planners follow, with data in thousands of dollars.

|Public Accountant |Financial Planner |

|30.6, 31.2, 28.9, 35.2, 25.1, 33.2, 31.3, 35.3, 31, 30.1, |31.6, 26.6, 25.5, 25, 25.9, 32.9, 26.9, 25.8, 27.5, 29.6, |

|29.9, 24.4 |23.9, 26.9, 24.4, 25.5 |

a. Using [pic], test for any difference between the population mean starting annual salaries for the two professions. What is your conclusion?

b. What is the point estimate of the difference between the two population means? Which profession has the higher mean annual starting salary?

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