This
paper presents four methods of constructing the confidence interval for the
proportion p of the binomial distribution. Evidence in the literature indicates the
standard Wald confidence interval for the binomial proportion is inaccurate,
especially for extreme values of p.
Even for moderately large sample sizes, the coverage probabilities of the Wald
confidence interval prove to be erratic for extreme values of p. Three alternative confidence
intervals, namely, Wilson confidence interval, Clopper-Pearson interval, and
likelihood interval, are
compared to the Wald confidence interval on the basis of coverage probability
and expected length by means of simulation.
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