The Internal Revenue Service (IRS) is conducting a study to determine the percentage of taxpayers who overpaid their taxes last year. In a sample of 2500 taxpayer returns, the IRS found that 780 taxpayers had overpaid.
a. Build a 99% confidence interval estimate of the percentage of all American taxpayers who overpaid their taxes last year and identify the margin of error for your interval.
b. If there are 180 million taxpayers in the US, show the 99% confidence interval estimate of the number of American taxpayers who overpaid their taxes last year and identify the margin of error for your interval.