Organizers of this year’s National Agricultural Board’s conference in Iowa City are planning to draw a simple random sample of participants to determine what proportion of them plan to return next year. How large a sample size would you recommend in order to ensure that, at the 95% confidence level, the actual proportion of all participants planning to return is no more than five percentage points (that is, +.05) away from the sample proportion that you produce, assuming
a. You have no idea what the returning proportion might be?
b. Your preliminary estimate is that 80% of this year’s participants will return?