One of the statistics that the College Board monitors is the rising tuition at private and public four-year colleges. The tuition and fees for private and public four-year colleges for the 1980–1981 academic year in 2005 dollars were $8,180 and $1,818, respectively. The file titled College$ contains data that yield the same average tuition and fees (adjusted for inflation) for private and public four-year colleges obtained by the College Board for 2005–2006.
a. Do the data indicate that the gap between tuition and fees at private and public colleges has more than doubled in the 2005–2006 academic year as compared to that of the 1980–1981 academic year? Use a significance level of 0.01. Assume the population variances are equal.
b. What statistical error could have been made based on the decision reached in part a? Provide an explanation.