An educational consulting group claims that there is a difference in the mean student loan debt of students who attended private four-year colleges and the mean student loan debt of students who attended public four-year colleges. The consulting group studied the student loan debt from private and public four-year colleges by collecting a random sample of loan debt from each type of college.
Assume that the amounts of student loan debt are normally distributed and that the population variances are not equal. At the 0.01 level of significance, is there sufficient evidence that the mean student loan debt for private four-year colleges is different from the mean student loan debt for public four-year colleges?
Let $\mu_1$ represent the mean for private four-year colleges and $\mu_2$ represent the mean for public four-year colleges.
With a p-value of approximately 0.00 and $\alpha = 0.01$, draw a conclusion and interpret the results of this hypothesis test.