A random sample of 2,750 students who majored in the social sciences found that 908 defaulted on their student loans, and a random sample of 3,560 students who majored in the physical sciences found that 1,245 defaulted on their student loans.

a. Is the loan default rate higher for students who major in the physical sciences as compared to the loan default rate for students who major in the social sciences?

b. How big of a sample would be needed to find a \(10 \%\) difference in student loan default rates based on the major?