It is difficult to conduct sample surveys on sensitive issues because many peopl

Question

It is difficult to conduct sample surveys on sensitive issues because many people will not answer questions if the answers might embarrass them. Randomized response is an effective way to guarantee anonymity while collecting information on topics such as student cheating or sexual behavior. Here is the idea. To ask a sample of students whether they have plagiarized a term paper while in college, have each student toss a coin in private. If the coin lands heads and they have not plagiarized, they are to answer "No." Otherwise they are to give "Yes" as their answer. Only the student knows whether the answer reflects the truth or just the coin toss, but the researchers can use a proper random sample with follow-up for nonresponse and other good sampling practices. Suppose that in fact the probability is 0.4 that a randomly chosen student has plagiarized a paper. Draw a tree diagram in which the first stage is tossing the coin and the second is the truth about plagiarism. The outcome at the end of each branch is the answer given to the randomized-response question.

What is the probability of a "No" answer in the randomized-response poll?

If the probability of plagiarism were 0.14, what would be the probability of a "No" response on the poll?

Now suppose that you get 32% "No" answers in a randomized-response poll of a large sample of students at your college. What do you estimate to be the percent of the population who have plagiarized a paper?

Explanation / Answer

the probability of a "No" answer in the randomized-response poll

= 0.5 *(1-0.4) = 0.5*0.6 = 0.3

If the probability of plagiarism were 0.14, the probability of a "No" response on the poll

= 0.5*(1 - 0.14) = 0.5* .86 = 0.43

suppose that you get 32% "No" answers in a randomized-response poll of a large sample of students at your college. let estimate to be the percent of the population who have plagiarized a paper

= p

so

0.5* (1 -p) = 0.32

hence

1- p = 0.64

p= 0.36

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