A survey conducted at a mid western university and involving 1,500 students found that 68% had taken out a student loan to help pay for the cost of their college education. A similar study at a southeastern university in which 2,000 students were surveyed found that 47% had taken out a student loan.
a. Develop and interpret a 95% confidence interval estimate for the difference in the proportions of students who have loans at these two universities.
b. Using an alpha level of 0.05, test the hypothesis that there is no difference in the proportions of students at these two universities who have loans. How does this test compare with the result you found in part a?