To use the large-sample confidence interval for a proportion, you need at least 15 outcomes of each type.

Show that the smallest value of n for which the method can be used is

(a) 30 when πˆ = 0.50,

(b) 50 when πˆ = 0.30,

(c) 150 when πˆ = 0.10.

That is, the overall nmust increase as πˆ moves toward 0 or 1. (When the true proportion is near 0 or 1, the sampling distribution can be highly skewed unless n is quite large.)

Select the best response in Exercises 5.66–5.69.