A sample of 65 male professors at a major four-year university produced a

mean annual pay of $74,800 and a standard deviation of $4,850. A sample of 60 female

professors at the same university produced a mean annual pay of $70,250 and a standard

deviation of $5,250. Does this constitute enough evidence to conclude that male and female

professors at this university are not paid the same?

(a) State the hypotheses.

(b) Using a 5% significance level, determine the rejection and non-rejection regions.

(c) Calculate the test statistic and the p-value, and interpret the results, and answer the

original question.

(d) Calculate the 95% confidence interval for the difference between the two population

means. How does this result relate to your conclusions in part (c)?