Question: 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?

1. 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 interpret the result, and answer the original research question.

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