Senior partners of an accounting firm are concerned about recent complaints by some female managers that they are paid less than their male counterparts. In response to these charges, the partners ask their human resources director to record the salaries of female and male managers with equivalent education, work experience, and job performance. A random sample of these pairs of managers is provided in the file P09_30.xlsx. That is, each male-female pair is matched in terms of education, work experience, and job performance.
a. Do these data support the claim made by the female managers? Report and interpret a p-value.
b. Assuming a 5% significance level, which values of the sample mean difference between the female and male salaries would support the claim of discrimination against female managers?