A survey is conducted in which a \"Yes-or-No\" question is asked. Respondents ma

Question

A survey is conducted in which a "Yes-or-No" question is asked. Respondents may be reticent to answer Yes when that is the true answer, and this reticence results in biased surveys. To mitigate this problem researchers sometimes use "Random Response Questions". For these questions the respondent is instructed to flip a coin whose outcome is not observed by the surveyor, to answer Yes if the coin is "heads" and to answer truthfully if the coin is "tails." Suppose that respondents follow these instructions and do, in fact, answer truthfully when the coin comes up tails. In a random response survey about stealing as a child, 5/8 of the respondents answer Yes to question. Estimate the fraction of the respondents who have stolen as a child?

Explanation / Answer

Since sample proportion is unbiased estimator of population proportion. Hence expected proportion of YES speaking=5/8.

Further out of this 5/8, 1/2 speaks YES due to coin. Hence the truthfully YES speakin proportion (5/8)-(1/2)=1/8. (answer)

Thank You.

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