This should be an easy question, but I can't think of how to answer it! I never did take enough stats. I'm looking at n = 77 returned surveys which come from a population of size 627. (At the moment I'm assuming that response is uncorrelated with the answers; it's actually somewhat reasonable in this case, and I don't have the background I'd need to assume otherwise!) Each survey contains count data: I have [ ] 0 [ ] 1 [ ] 2 [ ] 3 foos (for various foo). From this I can of course determine the number of foos in the sample, and the BLUE for the total across the population. But what sort of distribution should I use to determine a (say) 90% confidence range? I was toying with misusing a Poisson model here (each respondent acting like a time interval), but even so I wasn't able to determine a CI (must have been doing something very wrong; when I did a normal approximation of the Poisson I came up with a negative lower bound!). In summary: 1. What sort of distribution is appropriate? A simpler one would be better. 2. Very briefly (one sentence or just drop in a link; I'll work out the details) how do I find a CI with that distribution?