At the last Board of Directors (BOD) meeting of a large enterprise, the Human Resources (HR) Director claimed that male middle managers were paid more annually than their female counterparts. The CEO of this enterprise requested a comparison of the annual salaries of female and male middle managers and to report back to the BOD. You have been tasked to conduct the study to validate the HR Director`s claim. Use a level of significance of 5%. A random sample of 40 middle managers was taken. These managers were separated in two groups (male and female) and their salaries were entered into Minitab and Excel. a. Using Minitab, do the appropriate hypothesis test for this study. i. Report your finding to the CEO by writing a one-paragraph report. ii. Explain why you did or did not choose the pooled t-test for your study. Your explanation needs to be supported with a boxplot and appropriate descriptive statistics. b. Calculate manually the 95% confidence interval. What are your findings? Do you come to the same conclusion that you did in (a)?

2. The Human Resources (HR) Director would like to implement a three-week training program for the manufacturing department employees, which she believes would improve their productivity. In order to have supporting data to support her belief, with the approval of the VP Operations, the three-week training program is given to 15 employees chosen randomly from the manufacturing department. We observed the number of items produced by these 15 employees before and after their training. The observation period before and after the training was 20 working days long. You have been tasked to conduct the study to validate the HR Director`s belief. Use a level of significance of 1%. a. Using Minitab, do the appropriate hypotheses test for this study. i. Report your finding to the HR Director by writing a one-paragraph report. ii. Are the two data sets independent or not? Explain your answer. b. Now show the manual calculations for the test in (a). You can use the Minitab descriptive statistics report to obtain the summaries to allow you to do the calculation. i. Do you come to the same conclusion that you did in (a)? c. Calculate manually the 99% confidence interval. What are your findings? Do you come to the same conclusion that you did in (a)?

3. Data on the one-year returns for a sample of financial sector equity funds are displayed below as percentages. We are interested in whether the typical return is positive. One-year returns (%): 4.64 1.37 3.15 3.39 -0.47 1.7 -2.81 5.14 2.97 4.17 (a) Explain whether a parametric test or a non-parametric test is more appropriate (b) Perform a Wilcoxon test manually to see if the median return for all financial services equity funds is indeed positive. Find the appropriate Wilcoxon critical value for the .05 level of significance. (c) Use the large-sample version of the Wilcoxon test to calculate a z-statistic for your result. What is the p-value? (d) Do the test on Minitab. How do the Minitab results support the earlier results in (b) and (c)?

4. Stocks are classified as conservative (C), moderately aggressive (M), or aggressive (A). Suppose a random sample of stocks from each of these categories was selected and the returns tracked over a six-month period. (a) Examine the data between conservative (C) and moderately aggressive (M) to determine which test would be more appropriate. (b) Regardless of your answer in (a), use a parametric test to test whether the data show evidence of real differences in average returns between conservative and moderately aggressive stocks. Use a level of significance of 5%. Show your intermediate calculations. (c) Perform the appropriate non-parametric test using Minitab to test for differences in the median returns between conservative and moderately aggressive stocks. Use a level of significance of 5%. Remember to do a complete test and use Minitab only as a calculator