Consider the 95% binomial score confidence interval for . When y = 1, show that the lower

Consider the 95% binomial score confidence interval for π. When y = 1, show that the lower limit is approximately 0.18/n; in fact, 0 < π < 0.18/n then falls in an interval only when y = 0. Argue that for large n and π just barely below 0.18/n or just barely above 1 – 0.18/n, the actual coverage probability is about e^–0.18 = 0.84. Hence, even as n →∞, this method is not guaranteed to have coverage probability ≥ 0.95 (Agresti and Coull 1998; Blyth and Still 1983).