A small pilot study estimated that 44% of all American adults agree that parents should be given vouchers that are good for education at any public or private school of their choice.

a. How large a random sample is required to obtain a margin of error of at most 0.03 with 99% confidence? Answer this question using the pilot study’s result as the guessed value for p̂.

b. Answer the question in part (a) again, but this time use the conservative guess p̂ = 0.5. By how much do the two sample sizes differ?