Statistics Q Watch
In trying to get honest answers to awkward questions, for example "Do you find Statistics interesting?” randomised responses are often asked for. Individuals are asked to toss a fair coin; if a head shows they answer the question "Do you find Statistics interesting?", but if a tail shows they answer another question "Were you born on a Sunday?”Assuming that one is equally likely to be born on each of the seven days of the week and
that the proportion of individuals finding statistics interesting is p, determine the probability of a positive response from a randomly chosen individual. If a (large) class of students resulted in 25 % of them giving positive responses, estimate the proportion who find statistics interesting.
1. You toss a coin
Heads->Do you find stats interesting? P(yes)=p and P(no)=1-P do not.
Tails->Were you born on a sunday? P(mon)=1/7 P(tues)=1/7 .....
=> Chance of tossing a coin and getting a "yes I like stats" response=1/2 x p = p/2
Large sample, 50% of them had the stats question, and 50% of them gave a "yes I like stats" response. So, *half* of the sample who answered the stats question liked stats, therefore because its a large sample, you can take p to equal a half.
Many thanks for your help. I do have one other question but i'll start a new thread for that.