A survey is to be taken, and one of the questions to be asked is, \"Have you eve

Question

A survey is to be taken, and one of the questions to be asked is, "Have you ever smoked marijuana?" If the respondent has smoked marijuana, she may concerned that a truthful response would lead to a prosecution and thus respond "no", leading to an inaccurate estimate of the proportion in the population who has smoked marijuana. The randomized response deasign was developed to provide better information for such questions. Here the respondent may be instructed to flip a coin, not allowing the interviewer to see the outcome. If the coin lands with the "head" up, the respondent is to respond "yes"; otherwise the respondent answers the question truthfully (when the coin lands with the "tail" side up). Let p be the proportion of the people in the popilation who have smoked marijuana, and suppose that 0.7 of the people respond "yes". What proportion of the population would be estimated to have smoked marijuana?

Explanation / Answer

Solution:

0.5 of the responses (heads) are worthless as all will say "yes"
0.2 from the remaining 0.5 (tails) have said "yes"
so p = 0.2/0.5 = 0.4

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