85. 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 two-tailed test is a level .01 test.

c. Sketch a graph of
(p ) as a function of p for this test.

Is this desirable?