According to a 2016 report from the Institute for College Access and Success 66% of all graduates from public colleges and universities had student loans. A public college surveyed a random sample of 400 graduates and found that 62% had student loans.

a. Test the hypothesis that the percentage of graduates with student loans from this college is different from the national percentage. Use a significance level of 0.05.

b. After conducting the hypothesis test, a further question one might ask is what proportion of graduates from this college have student loans? Use the sample data to find a 95% confidence interval for the proportion of graduates from the college who have student loans. How does this confidence interval support the hypothesis test conclusion?