What is 95% confidence interval for the fraction of 5 successes out of 12 trials?
Is it possible to compute confidence intervals for a sample of this size?
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It is certainly possible to do this. There are several methods. The literature is surprisingly large; for a good entry point see Agresti & Coull (1998)
If you are using
R you can use this:
install.packages("binom") library(binom) binom.confint(5, 12)
binom package, just run the following to get the 95% confidence interval using the "exact" method (Clopper-Pearson method)
binom.test(x = 5, n = 12)$conf.int # same as binom::binom.confint(x = 5, n = 12, methods = "exact")