The American Association of University Professors (AAUP) conducts salary studies of college professors and publishes its findings in AAUP Annual Report on the Economic Status of the Profession. In Example 10.3 on page 399, we performed a hypothesis test based on independent samples to decide whether mean salaries differ for faculty in private and public institutions. Now you are to perform that same hypothesis test based on a paired sample. Pairs were formed by matching faculty in private and public institutions by rank and specialty. A random sample of 30 pairs yielded the data, in thousands of dollars, presented on the WeissStats CD. Use the technology of your choice to do the following tasks.
a. Decide, at the 5% significance level, whether the data provide sufficient evidence to conclude that mean salaries differ for faculty in private institutions and public institutions. Use the paired t-test.
b. Compare your result in part (a) to the one obtained in Example 10.3.
c. Repeat both the pooled t-test of Example 10.3 and the paired t-test of part (a), using a 1% significance level, and compare your results.
d. Which test do you think is preferable here: the pooled t-test or the paired t-test? Explain your answer.
e. Find and interpret a 95% confidence interval for the difference between the mean salaries of faculty in private and public institutions. Use the paired t-interval procedure.
f. Compare your result in part (e) to the one obtained in Example 10.4 on page 402.
g. Obtain a normal probability plot and a boxplot of the paired differences.
h. Based on your graphs from part (g), do you think that applying paired t-procedures here is reasonable?