Question 1 Board of Directors (BOD) - [16 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 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 1%. A random sample of 46 middle managers was taken. These managers were separated in two groups (male and female) and their salaries were entered into Minitab and Excel.

a. Perform manually the appropriate parametric hypothesis test for this study. Check your results using software.

1. Report your findings to the CEO by writing a one-paragraph report.

2. 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.

3. Calculate manually the corresponding 99% confidence interval for the difference in the mean annual salaries between male and female middle managers. What are your findings? Do you come to the same conclusion that you did in part (a)?

4. Perform manually the appropriate non-parametric test for the difference in the median annual salaries between male and female middle managers. Use a level of significance of 1% and clearly state the sums of the ranks (T1 and T2) and the corresponding p-value. Remember to do a complete test and confirm your results using software.

   Hint: Since sample sizes are larger than 10, use the normal approximation discussed in class.

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