1
$\begingroup$

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!

| cite | improve this question | |
$\endgroup$
  • $\begingroup$ 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 '15 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 '15 at 14:13
0
$\begingroup$

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.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.