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Unformatted text preview: DEPARTMENT OF ECONOMICS ECON 131A YALE UNIVERSITY ECONOMETRICS & DATA ANALYSIS I FALL 2010 Assignment #5 For Practice: Not to be handed in PLEASE NOTE: We will do question 1 in class on Thursday October 7, and questions 2-3 on Tuesday October 12. Questions 4-9 are practice problems on hypothesis testing. Solutions are posted on the web. QUESTIONS 1-3 will be covered in class. 1. In the U.S., there are two sources of national statistics on crime rates: ( i ) the FBI’s Uniform Crime Reporting Program, which publishes summaries on all crimes reported to police agencies in jurisdictions covering virtually 100% of the U.S.; ( ii ) the National Crime Survey (NCS), which is based on interviews with a nationwide probability sample of households. In 1992, 4.9% of the households in the NCS sample told the interviewers they had experienced a burglary within the past 12 months. The same year, the FBI reported a burglary rate of 32 per 1,000 households, or 3.2%, for the U.S. as a whole. If the FBI’s 3.2% figure is the true burglary rate for the population of U.S. households in 1992, what is the probability that the National Crime Survey would obtain a result of 4.9% or more? You may assume that the NCS is based on a simple random sample of 50,000 households out of a population of 100 million households. What do you conclude? 2. Each year, the Internal Revenue Service attempts to estimate total tax com- pliance: whether Federal tax revenues are above or below what they should be, and by how much. For many years, this was performed by the IRS Tax Compliance Measurement Program (TCMP). To conduct the TCMP, the IRS draws a simple random sample of U.S. citizens and audits each one. In a TCMP audit, the true tax liability of the individual (or household, if the indi- vidual files Federal income taxes jointly with a spouse) is assessed by the IRS after detailed examination of the individual’s (or household’s) total income by IRS agents. The tax liability determined in the audit is then compared to the actual tax return filed by the individual or household. The IRS extrap- olates from the average tax underpayment in the TCMP sample to estimate 1 the total personal income tax underpayment level in the U.S. Until recently,the total personal income tax underpayment level in the U....
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- Taxation in the United States, Statistical hypothesis testing, Simple random sample, Income tax in the United States