Percentage of Marijuana smokers

[crisi]

To get answers to sensitive questions, we sometimes use a method called the
randomized response technique. Suppose, for instance that we want to determine what
percentage of students at a University who 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 1 of the 20 cards at random and respond
“yes” or “no” without divulging the question. (2.112)
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 U of
G smokes marijuana at least once a week.
b. If 106 of 250 students answered “yes” under these conditions so that 106/250 is
your estimate of P(Y), what is your estimate of P(M)?