The Congressional Subcommittee on Taxation is interested in estimating the proportion of taxpayers who took advantage of the newly modified mortgage interest deduction on their most recent federal tax returns.
a. If the subcommittee wants the estimate to be within four percentage points of the actual population proportion at the 95% confidence level, how large a sample of tax returns should they select? Assume no prior information.
b. Suppose the subcommittee wants to reduce the margin of error term to two percentage points (.02), but doesn't want to increase the sample size determined in part a. What confidence level would they have to settle for?