To get answers to sensitive questions, we some-times use a method called the randomized response technique. Suppose, for instance, that we want to determine what percentage of the students at a large university smoke marijuana. We construct 20 flash cards, write “ I smoke marijuana at least once a week” on 12 of the cards, where 12 is an arbitrary choice, And “ I do not smoke marijuana at least once a week” on the others. Then, we let each student (in the sample interviewed) select one of the 20 cards at random And respond “ yes” or “ no” without divulging the question.
(a) Establish a relationship between P(Y) , the probability that a student will give a “ yes” response, And P(M) , the probability that a student randomly selected at that university smokes marijuana at least once a week.
(b) If 106 of 250 students Answered “ yes” under these conditions, use the result of part (a) And 106/250 as an estimate of P(Y) to estimate P(M) .