A researcher wishes to estimate, with 99% confidence, the population proportion of adults who think Congress is doing a good or excellent job. Her estimate must be accurate within 5% of the true 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 40% of the respondents said they think Congress is doing a good or excellent job.

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