A sample of 85 male professors at a major four-year university produced a mean annual pay of $75,600 and a standard deviation of $4,550. A sample of 80 female professors at the same university produced a mean of $68,250 and a standard deviation of $6,250. 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 interpret the result.
(d) Calculate the p-value, and interpret the result.
(e) Construct a 95% confidence interval for the difference between the two means, and interpre the result, and answer the original research question.
Details are welcome, as much as possible.