Consider the Large-Sample Level $H _ { 0 } : p = .2$

Essay

Consider the large-sample level .01 test for testing $H _ { 0 } : p = .2$ versus $H _ { a } : p > .2$
a. For the alternative value p = .21, compute $\beta ( .21 )$
sample sizes n = 100, 2500, 10,000, 40,000, and 90,000.
b. For $\hat { p } = x / n = .21$
, compute the p-value when n = 100, 2500, 10,000, and 40,000.