Suppose that as part of a study on student loan debt, a national agency that underwrites student loans is examining the differences in student loan debt for undergraduate students. One question the agency would like to address specifically is whether the mean undergraduate debt of nonminority students is less than the mean undergraduate debt of minority students. To conduct the study, suppose that a random sample of 92 nonminority students and a random sample of 110 minority students who completed an undergraduate degree were taken. The undergraduate debt incurred for financing college for each sampled student was collected. The sample results can be found in the file Student Debt.

a. Assume that the agency believes the two populations from which the samples were taken are approximately normally distributed with equal variances. Conduct a hypothesis test at the 0.01 level of significance to determine whether the mean undergraduate debt for nonminority students is less than the mean undergraduate debt for minority students.

b. For what values of alpha would your decision in part a change?

c. Suppose the agency is unwilling to assume the two populations from which the samples are taken are approximately normally distributed with equal variances. Conduct the appropriate test to determine whether the mean undergraduate debt for nonminority students is less than the mean undergraduate debt for minority students. Use the p-value approach to conduct the test. State a conclusion.