Suppose you want estimate the proportion of traditional college students on your campus who own their own cars. You have no preconceive idea of what the proportion might be.

a) What sample size is needed if you wish to be 95% confident that your estimate is within 0.02 of the true proportion?

b) What sample size is needed if you wish to be 99% confident that your estimate is within 0.02 of the true proportion?

c) What sample size is needed if you wish to be 95% confident that your estimate is within 0.05 of the true proportion?

d) What if you know from some prior research on other college campuses that you believe the proportion will be near 20%. How would a), b), and c) change?