Consider the Wald confidence interval for a binomial parameter π.

Consider the Wald confidence interval for a binomial parameter π. Since it is degenerate when π̂ = 0 or 1, argue that for 0 < π < 1 the probability the interval covers π cannot exceed [1 –πn – (1–π)n]; hence, the infimum of the coverage probability over 0 < π < 1 equals 0, regardless of n.

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