A consumer agency wants to estimate the proportion of all drivers who wear seat belts while driving.

a) Suppose that, in a preliminary study, 76% of the drivers wore seat belts while driving. How large should the sample size be so that the99% confidence interval for the population proportion has a margin of error of .03?

b) What is the most conservative estimate of sample size needed so that the 99%confidence interval for the population proportion has a margin of error of .03?