# survey - of this survey Suppose N persons were selected for...

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A Survey to Estimate Tax Evasion Consider the problem of estimating the fraction of people who cheat on their taxes by survey a randomly selected sample of people. If you ask this question to a person “Does he/she cheat on the taxes?” , then you are not going to ever get the correct answer. Therefore, we use the following strategy to do this survey (say over a telephone). 1. The person is asked to ﬂip a coin. 2. If the coin turns up heads, then the person should answer YES . 3. Else, answer the question correctly. In this survey, the person does not feel threatened in giving the correct answer if he/she cheated on his/her taxes. Now let us consider the problem of estimating the fraction of people who cheat on their taxes from the results

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Unformatted text preview: of this survey. Suppose N persons were selected for the survey and n of them answered YES . Also, let us assume that the fraction of people who cheat on their taxes is p . Also, let us deﬁne events A and B as A ← Event that Answer = YES B ← Event that the Toss = Heads Now, P ( A ) = P ( A ∩ B ) + P ( A ∩ B c ) (1) = P ( B ) · P ( A | B ) + P ( B c ) · P ( A | B ) (2) = 1 2 · 1 + 1 2 · p (3) = p + 1 2 (4) Therefore, p +1 2 = n N which implies p = 2 n-N N . 1 Note that 2 n > N because at least half of the people will answer YES as half of the people will get a Heads as their coin toss. Therefore, you have estimated the fraction p of people who cheat on their taxes using this survey. 2...
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## This note was uploaded on 10/05/2010 for the course BUS 1142 taught by Professor Miller during the Fall '10 term at Carnegie Mellon.

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survey - of this survey Suppose N persons were selected for...

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