In order to devise a marketing strategy, the manufacturer of a new drug used for pain relief in patients with arthritis needs to obtain an estimate for the population proportion, p , of users of the drug who will experience temporary pain relief. In order to get an indication of what a plausible value for p would be, an analyst decides to give the drug to a random sample of people who suffer from arthritis pain and determine the sample proportion, p hat, who experience temporary pain relief. The sample proportion will then be used as the basis for a confidence interval for the population proportion:

(a) The analyst wants to compute a 95% confidence interval for the population proportion that has a sampling error (SE) which does not exceed .025. Since this is a new drug, the analyst chooses not to speculate on what the value of the population proportion might be. What is the smallest sample size that could be used that would meet these requirements for the confidence interval?