In preparing a report on the economy, we need to estimate the percentage of businesses that plan to hire additional employees in the next 60 days.

I have been asked to answer the following fully, and show all my work.

a) How many randomly selected employees must we contact in order to come up with an estimate in which we are 98% confident with a margin error of 5%?

b) Suppose we want to reduce the margin error to 3%. What sample size will suffice?

c) Why might it not be worth the effort to try to get an interval with a margin of error of only 1%?