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...
thanks in advance for help!