Question 7.50

image 20. Randomized response: Suppose 30 students in a class participate in a survey in which they each flip a coin and do not reveal the result. If the result is tails, the student is supposed to give an honest answer to the question “Have you ever used a fake ID?” If the result is heads, the student is supposed to say “yes” to that question, regardless of what the true answer is. Suppose the results in the class are 18 “yes” answers and 12 “no” answers.

  1. If students follow the procedure correctly, is it true that all students who answered “no” have not used a fake ID?
  2. If students follow the procedure correctly, is it true that all students who have not used a fake ID answered “no”?
  3. On average, about half of the students who have not used a fake ID flipped tails, so what is your best estimate of the true number of students who have not used a fake ID?
  4. Based on the answer to part (c), what is your estimate of the true number and proportion of students who have used a fake ID?
  5. Do we have any way to know which of the 18 “yes” answers are truthful?