Although not all students have debt after graduating from college, more than half do. 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 might have been used to determine this difference in which the private, for-profit colleges’ 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. Examine the sample standard deviations. What do these suggest is the relationship between the two population standard deviations? Support your assertion.
b. Conduct a hypothesis test to determine if the average college debt for bachelor of arts degree recipients is at least $25,000 more for graduates from private colleges than from public colleges. Use a 0.01 significance level and a p-value approach for this hypothesis test.