You wish to estimate, with 99% confidence, the population proportion of U.S. adults who think that foods containing genetically modified ingredients should be labeled. Your estimate must be accurate within 2% of the population proportion.

(a) No preliminary estimate is available. Find the minimum sample size needed.

(b) Find the minimum sample size needed, using a prior study that found that 87% of U.S. adults think that foods containing genetically modified ingredients should be labeled.

(c) Compare the results from parts (a) and (b).