How do consumers feel about companies sharing and selling their personal data? A Bain & Company press release (bit.ly/1FZ1QCH) reports that a new survey they conducted found that 67% of consumers indicate that it should be illegal for companies to collect or use such data without getting prior consent.

a. To conduct a follow-up study that would provide 99% confidence that the point estimate is correct to within {0.03 of the population proportion, how many consumers need to be sampled?

b. To conduct a follow-up study that would provide 99% confidence that the point estimate is correct to within {0.05 of the population proportion, how many consumers need to be sampled?

c. Compare the results of (a) and (b).