1. 5.30 You are interested in assembling a random sample of young people that occasion ally use soft drugs. To prevent people from falsely claiming not to use soft drugs, you have thought of the following procedure. The interviewer asks each young person to toss a coin, keeping the result of the toss a secret. The young person is then instructed that if he/she tosses heads he/she must answer “yes” to the question asked even if the true answer to the question is “no” and that if he/she tosses tails, he/she must simply answer the question with the truth. Suppose that the random sample consists of n young people. Let Xi equal 1 if the ith person answers “yes”

and otherwise let Xi be equal to 0. Verify that the unknown value of the fraction of young people that use soft drugs can be estimated by 2 sponding95%confidenceinterval2 X(n) −1 ±1.96 ×2 X(n) −1withthe corre X(n)]/√

X(n)[1 −

n.