Suppose a study has been conducted to determine whether there is a difference between student debt at private, for-profit universities and public universities.

It was found from random samples that the private, for-profit colleges’ average debt was $38,300 and the public colleges average was $11,800. The respective standard deviations were $2,050 and $2,084. The sample sizes were 75 and 205, respectively.

Conduct a hypothesis test to determine if the average student debt 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. Assume equal population variances.