#29: A quality inspector is interested in the time spent replacing defective parts in one of the company's products. The average time spent should be at most 20 minutes (min) per day according to company standards. The following hypotheses are set up to examine whether the standards are being met:

\(\begin{aligned}

&H_{0}: \mu \leq 20 \\

&H_{a}: \mu>20

\end{aligned}\)

where \(\mu\) represents the population average time spent replacing defective parts. To conduct the test, a random sample of 16 employees is chosen. The average time spent replacing defective parts for the sample was \(20.5 \mathrm{~min}\), with a sample standard deviation of \(4 \mathrm{~min}\). Perform the test at a \(5 \%\)

level of significance. Assume the population of service times is approximately normally distributed. State the decision rule, the test statistic, and your decision. Are company standards being met?

#31: Refer to the data in Exercise 26. The July 1, 2002 , one-year returns for a random sample of 83 mutual funds are available in a file named ONERET2. The return for the S\&P 500 stock index for the same one-year time period was \(-18.0 \%\). Test to see if there is evidence that the average one-year return for the population of funds is more than the return for the S\&P 500 stock index. Use a \(5 \%\) level of significance. State the hypotheses to be tested, the decision rule, the test statistic, and your decision. What is your conclusion regarding the average one-year return for mutual funds?

#32: A graduate school of business is interested in estimating the difference between mean GMAT scores for applicants with and without work experience. Independent random samples of 50 applicants with and 50 applicants without work experience are chosen. The following results were obtained:

Construct a \(95 \%\) confidence interval estimate of the difference between the mean GMAT scores for the two groups.

#35: The one-year returns for a random sample of 51 load mutual funds and 32 no-load funds were obtained. The returns are in a file named RETURNS2. Construct a \(95 \%\) confidence interval estimate of the difference between the population mean returns.

These data are arranged in the file in two columns. The first column contains the returns for the funds and the second column indicates to which sample ( load \(=1\), no-load \(=0\) ) each value in column 1 belongs (in the Excel spreadsheet, the returns are in two separate columns).

#39. Use the information in Exercise 34. Is there a difference in population mean rating scores for the two divisions? State the hypotheses to be tested, the decision rule, the test statistic, and your decision. Assume that the population variances are equal and the populations are normally distributed. Use a \(5 \%\) level of significance.

#40) The 1 -year returns for a random sample of 51 load mutual funds and 32 no-load funds were obtained. Test to see if there is any difference between the population average 1-year returns for load and no-load funds. Use a \(5 \%\) level of significance. State the decision rule, the test statistic, and your decision. Is there a difference in the population averages? Based on the test results, what conclusions do you draw concerning investment in load versus no-load funds? The returns are in a file named RETURNS2. See Exercise 35 for a further description of the data in the file.

#43) Consider again the finance and marketing starting salaries in Exercise 42 .

1. Conduct a test to determine whether the population mean starting salaries for the two majors are equal. State the hypotheses to be tested, the decision rule, the test statistic, and your decision. Use a \(5 \%\) level of significance.
2. What conclusion can be drawn from the result in part a?

#45) The file named HARRIS2 contains 1977 annual starting salary data for 93 employees of Harris Bank of Chicago. The column of data denoted MALE indicates whether the employees were MALE(1) or FEMALE(0) (in the Excel spreadsheet, the salary data are in two separate columns.) Let \(\mu_{0}=\) average starting salary for females and \(u_{1}=\) average starting salary for males.

1. Set up and test hypotheses to determine whether there is evidence of wage discrimination for the Harris Bank employees. Use a \(5 \%\) level of significance. Set up the hypotheses assuming that discrimination is represented by an average wage for females that is less than the average wage for males.

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