Question
webassign.net It is difficult to conduct sample surveys on sensitive issues se many people will not answer questions if the answers might embarrass them . Randomized response is an ation 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 Othe college, have each student toss a coin in private. If the coin lands heads and they have not plagiarized, they are to answer "No. erwise they are to give "Yes as their answer. Only the student knows whether the answer reflects the truth or just the coln toss, but the researchers random sample with follow-up for nonresponse an 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 can use a proper d other good sampling practices. Suppose that in fact the probablity is 0.3 that a randomly chosen student has plaglarized a to the randomized-response question. Ileads Tails 05 .5 Yes,0 3 .3 0.5 What is the probability of a "Nor answer in the randomized-response po? 0.35 If the probability of plagiarism were 0.24. what would be the Probability ota Noi ftrponse on the Poil? 0.38 n ora large sample of student s at your college. what do you estimate to be the percent of the Now suppose that you get 32% "No-answers in a rando
Explanation / Answer
in the tree
the first box corresponding to No will be 1 -0.3 = 0.7
the lowest box corresponding to No will be 0.7 *0.5 = 0.35
the other box will be 0.5*0.3 = 0.15
a) probability of No= 0.35
b) if probability of plagiarism = 0.24
then probability of No = 0.5 * (1 - 0.24 ) = 0.38
c)
let the probability of plagiarism = p
then 0.5 *(1-p)= 0.32
1-p = 0.64
p = 0.36
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