Using the delta method, show that the Wald confidence interval for the logit of a binomial parameter is log [/(1)] z /2 /n(1).

Using the delta method, show that the Wald confidence interval for the logit of a binomial parameter π is log [π̂/(1–π̂)] ± z_α/2/√nπ̂(1–π̂). Explain how to use this interval to obtain one for π itself. [Newcombe (2001) noted that the sample logit is also the midpoint of the score interval for π, on the logit scale. He showed that this logit interval contains the score interval.]