93. 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 the alternative Ha: 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 twotailed test is a level .01 test.

c. Sketch a graph of b(p) as a function of p for this test. Is this desirable?