Getting responses to sensitive questions in a survey is difficult. Suppose you are doing a survey on illicit drug use and want survey participants to answer the following question: Q1: Have you ever used marijuana?
This is a sensitive question and participants may be reluctant to answer the question truthfully. To alleviate their fears, you do the following in the survey. Each participant flips a coin (only the participant knows the outcome of this toss; you do not get to observe the toss). If it lands heads, the participant answers Q1. If it lands tails, the participant answers Q2: Q2. Is the seconds hand of your watch between 0 and 30 at this moment? So, each participant answers either Q1 or Q2 depending on the outcome of their toss. Others do not know which question they answered. Since data collector does not know which question is being answered, it is hoped that survey participants answer the sensitive question truthfully. Suppose 100 people participated in the survey and 60 of them answered yes. How can you use this information to estimate the proportion of individuals that have used marijuana?