Consider the 95% binomial score confidence interval for π. When y s1, show that the lower limit is approximately 0.18/ n ; in fact, 0

Consider the 95% binomial score confidence interval for π. Whenys1, show that the lower limit is approximately 0.18/n; in fact, 0<π><>nthen falls in an interval only wheny=0. Argue that for largenand π just barely below 0.18/nor just barely above 1=0.18/n, the actual coverage probability is aboute
^-0.18 =0.84. Hence, even asn→∞, this method is not guaranteed to have coverage probability ≥0.95(Agresti and Coull 1998; Blyth and Still 1983).