In Example 9.2.15 it was shown that a confidence interval for a Poisson parameter can be expressed in terms of chi squared cutoff points. Use a similar technique to show that if X ~ binomial(n, p), then a 1 - α confidence interval for p is

where Fv1, v2, α is the upper a cutoff from an F distribution with v1 and v2 degrees of freedom, and we make the endpoint adjustment that the lower endpoint is 0 if x = 0 and the upper endpoint is 1 if x = n. These are the Clopper and Pearson (1934) intervals.

2 2(n+1),2z,a/2