The Internal Revenue Service collects personal income and corporate taxes. Most of the job involves processing the paperwork that accompanies taxes. The IRS verifies, for example, the reported Social Security numbers and compares reported earnings from W-2 and 1099 forms to the earnings reported by each taxpayer. Forms with errors or discrepancies lead to follow-up letters and, in some cases, the dreaded IRS audit. The IRS has limited personnel and cannot audit every taxpayer€™s return. Sampling is a necessity. The IRS temporarily stopped doing audits for a few years, but resumed auditing random samples of tax returns in 2007.9 Concerns about a growing €˜tax gap,€™ the difference between what the IRS claims is owed and the amount paid, pushed the IRS to continue audits.
Motivation
(a) Why is it important for the IRS to audit a sample of all returns, not just those flagged as having an anomaly?
Method
(b) For certain types of audits, an agent visits the residence of the taxpayer. What sort of sampling method is well suited to audits that require a personal visit?
(c) If the IRS selects a sample of income tax forms for inspection at random, most will be from individuals with earnings below $100,000. According to the U.S. Census, about 85% of households earn less than $100,000 and half earn less than $50,000. If the IRS would like to have 30% of the audited tax returns cover households that earn more than $100,000 (with the rest chosen at random), how should it choose the sample?
Mechanics
(d) If the IRS selects 1,000 personal income tax returns at random from among all submitted, will it obtain a random sample of taxpayers for this year? (Note: Married couples typically fle a joint return.)
(e) An auditor selected a random sample of returns from those submitted on April 15, typically the last day that returns can be fled without a penalty. Explain why these are not a representative sample of all of the returns.
Message
(f) If the IRS is interested in finding and discouraging tax cheats, what sort of sampling methods should it advertise in press releases?

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国Microsatt Excel Tax Compliance in the United States (billions of dollars) 2006 Gap Paid 10 12 13 14 15 16 17 2001 Gap Paid 19 S0 $500 $1,000 $1.500 $2,000 $2,500