A company has received complaints about its customer service. The managers intend to hire a consultant to carry out a survey of customers. Before contacting the consultant, the company president wants some idea of the sample size that she will be required to pay for. One value of interest is the proportion p of customers who are satisfied with the company's customer service. She decides that she wants the estimate to be within 3 percentage points (0.03) at a 99% confidence level.

1. Using a conservative estimate for p,, how large of a sample is needed?

2. In the company's prior-year survey, 85% of customers surveyed said they were satisfied. Using this value as a guess for p,, find the sample size needed for a margin of error of at most 3 percentage points with 99% confidence. How does this compare with the required sample size from question #1?

3. What if the company president demands 95% confidence instead of 99% confidence? Would this require a smaller or larger sample size, assuming everything else remains the same? Explain your answer.