Suppose that the proportion p of defective items in a large population of items is unknown, and that it is desired to test the following hypotheses:
H0: p = 0.2,
H1: p = 0.2.
Suppose also that a random sample of 20 items is drawn from the population. Let Y denote the number of defective items in the sample, and consider a test procedure δ such that the critical region contains all the outcomes for which either Y ≥ 7 or Y ≤ 1.
a. Determine the value of the power function π(p|δ) at the points p = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1; sketch the power function.
b. Determine the size of the test.