A government wants to find out how many of its citizens are filling out fraudule
ID: 3273196 • Letter: A
Question
A government wants to find out how many of its citizens are filling out fraudulent tax returns but knows that for obvious reasons it is hard to ask people to directly reveal what they do. It creates a survey with the single question “Do you fill out your tax return honestly? Answer Yes or No” Along with the question come the following Instructions: Toss a fair coin. If the result of the coin toss is heads, answer the question truthfully. If the result of the coin toss is tails, answer the question with NO regardless of whether you cheat or not. Randomising the response makes it impossible to deduce for any single individual that they cheat. The result of the survey is that 45% of the respondents say YES. Suppose we interpret this as meaning that a randomly chosen member of the population will answer the survey YES with probability 0.45. Find the proportion of the population that fills out fraudulent
Explanation / Answer
Let p be the proportion of people who fill out fraudulent tax returns
Total proportion of NO expected = P(heads)x(1-p) + P(tails)
0.5(1-p) + 0.5
Given proportion of NO = 1 -0.45 = 0.55
0.5 (1-p) + 0.5 = 0.55
0.5(1-p) = 0.05
(1-p) = 0.1
p = 0.9
90% of population fills out fraudulent forms