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 Hispanic students graduating in 2009 is less than the mean undergraduate debt of Asian-American students graduating in 2009. To conduct the study, a random sample of 92 Hispanic students and a random sample 110 Asian-American students who completed an undergraduate degree in 2009 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 Hispanic students is less than the mean undergraduate debt for Asian-American 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 Hispanic students is less than the mean undergraduate debt for Asian-American students. Use the p -value approach to conduct the test. State a conclusion.