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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!

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  • $\begingroup$ 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 $\sum_{i = 1}^{10} p_i/10$? $\endgroup$
    – P.Windridge
    Apr 10, 2015 at 10:04
  • $\begingroup$ I am assuming the probability is equal, but because the coins are actually people pressing either 1 or 2, some of them might for example have a bias (say, toward the "1" key) $\endgroup$
    – reddawg50
    Apr 10, 2015 at 14:13

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I think that if you consider all your coins to be non-biased, or all equally-biased, then it would not be a problem to consider your 500 flips as though they came from the same coin. Theoretically, the probability for every flip is still .5 for heads, .5 for tails.

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