# appropriate binomial proportion confidence interval for repeated measures

So I have looked this up extensively and keep getting the same answer, but its because what I can find online isn't quite to the point. I want to put a confidence interval on a binomial proportion, but its not the 'classic case' where you have, say, 50 people who said 'yes or no' to a single question and you want a confidence interval on the mean number of 'yes' responses.

Instead, imagine that I've flipped a coin 50 times. And then I flip 9 more coins 50 times each. What is the correct way to put a confidence interval around the grand mean from all 500 trials?? I.e. it seems that we should not treat it as if I had flipped one coin 500 times, nor that I flipped 500 coins one time each...

• Are you assuming all the coins have the same probability of landing heads? (I assume all the flips are independent). If not, are you asking about the case that coin $i$ has probability $p_i \in (0,1)$ of coming up heads and you want confidence intervals for an estimate of $\sum_{i = 1}^{10} p_i/10$? Apr 10, 2015 at 10:04