The College Board’s 2008 Trends in Student Aid addresses, among other topics, the difference in the average college debt accumulated by undergraduate bachelor of arts degree recipients by type of college for the 2006–2007 academic year. Samples were used to determine this difference, in which the private, forprofit college average was $38,300 and the public college average was $11,800. Suppose the respective standard deviations were 2,050 and 2,084. The sample sizes were 75 and 205, respectively.

a. To determine which hypothesis test procedure needs to be used to decide if a difference exists in the average undergraduate debt between private and public colleges, one of the verifications that must be performed is whether the population variances are equal. Perform this test using a significance level of 0.10.

b. Indicate the appropriate test that should be used to determine if a difference exists in the average undergraduate debt between private and public colleges.