Statistical poll question

Question

I interviewed 100 people. I asked them to look at a photograph of 2 men. One is 17 years old and the other is 20 years old. The people interviewed had to guess who was the older looking man in the photograph. 76 people chose the man on the right as the older man. What conclusion, if any, can I conclude regarding who is older? For example, tell me something like, “I can only guess that the man on the right is probably older”. Or tell me specifically, using percentage confidence levels. That is, the man at the right is older at a confidence level of 76%. Thanks.

Answer 1

If your alt hypothesis is that the true probability of success is not equal to 0.5, and assuming that the 76 who chose the man on the right were, in fact, correct, you could do a 2-sided binomial test. The results are a p-value of <0.001 and the 95% CI is 0.66 - 0.84. In other words, people appeared to have been generally able to identify the older man; you're highly unlikely to get these results if people were completely unable to make the distinction.

Note that the poll appears to be flawed, however, as you didn't (?) randomize the position of the two men. Let me know if you need more details or you want to know how to run a binomial test in R.