In Example 9.2.5 a lower confidence bound was put on p, the success probability from a sequence of Bernoulli trials. This exercise will derive an upper confidence bound. That is, observing X1,..., Xn, where Xi ~ Bernoulli(p), we want an interval of the form [0, U(x1 ... ,xn,)), where Pp[p ∈ [0,U(X1,..., Xn))) ≥ 1 - α.
a. Show that inversion of the acceptance region of the test
H0: p = p0 versus H1: p < p0
will give a confidence interval of the desired confidence level and form.
b. Find equations, similar to those given in (9.2.8) that can be used to construct the confidence interval.