A local radio station is interested in estimating the percentage of a target market that has a favorable impression of its morning show. The marketing department wishes to estimate this proportion within ±0.02 of the true population value and have a confidence level of 95%. A pilot sample of 30 people was selected, and the proportion in this sample with a favorable impression was 0.55.
a. Based on this information, how many more people must be surveyed?
b. Determine the margin of error in the pilot sample. Assume a confidence level of 95%.
Suppose the station managers can't afford to survey as many people as required and have indicated that the maximum sample size can be 800 people. Assuming that the sample size is cut to 800:
c. Without changing the confidence level, indicate specifically what must be changed and by how much.
d. Without changing the margin of error, indicate specifically what must be changed and by how much.