After a period of apprenticeship, an organization gives an exam that must be passed to be eligible for membership. Let p = P(randomly chosen apprentice passes). The organization wishes an exam that most but not all should be able to pass, so it decides that p = .90 is desirable. For a particular exam, the relevant hypotheses are H₀: p = .90 versus H_a: ≠ p .90. Suppose ten people take the exam, and let X = the number who pass.

a. Does the lower-tailed region {0, 1, …,5} specify a level .01 test?
b. Show that even though Ha is two-sided, no two-tailed test is a level .01 test.

c. Sketch a graph of power as a function of p′ for this test. Is this desirable?