QUESTION 1 - BOARD OF DIRECTORS (BOD) - [32 MARKS]

At the last Board of Directors (BOD) meeting of a large enterprise, the Human Resources (HR) Director claimed that male middle managers were paid the same as their female counterparts. The CEO of this enterprise requested a comparison of the annual salaries of the female and male middle managers and to report back to the BOD.

You have been tasked to conduct the study to validate the HR Directors' claim. Use a level of significance of 5%. A random sample of 52 middle managers was taken. These managers were separated into 2 groups (male and female) and their salaries are as followed:

Male	Female
40621	41655
40675	41551
41123	40650
41560	41160
41720	40706
42175	41684
41870	40674
41942	39844
40250	40425
40804	41302
43300	42300
41655	40755
41325	40796
40499	40425
40802	40530
42050	40628
42086	40625
40512	41290
40742	39945
41426	40424
42492	40425
40747	41325
42497	40440
40499	40425
42050	40628
41426	40424

a. Perform the appropriate parametric hypothesis test for this study using Excel and check your calculations manually:

1. 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 obtained from Excel.
2. Report your findings to the CEO by writing a one-paragraph report. You must provide the following:

• Is the HR Director right?
• Provide a statement to explain the result (use p-value to explain)
• What kind of test did you use to solve this problem? Explain why.
• How many degrees of freedom did you use? Explain why.

b. Find the corresponding 95% confidence interval for the difference in the mean annual salaries between the male and the female middle managers using Excel. What are your findings? Check your results using manual calculations. Do you come to the same conclusion that you did in part a.?

c. Using a significance level of 5%:

1. Perform the appropriate nonparametric test for the difference in the median annual salaries between male and female middle managers using Excel.
2. Perform manually the appropriate nonparametric test for the difference in the median annual salaries between male and female middle managers. Clearly state the sums of the ranks (T1 and T2) Since sample sizes are larger than 10, use the normal approximation to find the p-value.
3. Provide a statement to explain the results (use the p-value to explain).