(adsbygoogle = window.adsbygoogle || []).push({}); Binomial distribution/confidence question for dummies

(The 'dummy' would be me.)

I have an event that happens with unknown probability p. Each of n independent events results in k of these events happening. How do I construct a (95%) confidence interval for p?

For small n it's easy to figure this out with numerical combinatorics:

Pr(at most k events) = [tex]\sum_{i=0}^k{n\choose i}p^i(1-p)^{n-i}[/tex]

Pr(at least k events) = [tex]\sum_{i=k}^n{n\choose i}p^i(1-p)^{n-i}[/tex]

and then find the roots of Pr(at most k events) - 0.05 and Pr(at least k events) - 0.05. (Maybe I should use 0.025 instead?)

But for large n (even not all that large!), this is inconvenient. Surely there is some standard statistical method for this? Sticking as close to the roots as possible would be best -- I'd prefer to use as little Central Limit Theorem as I can.

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# Distribution/confidence question for dummies

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