After a period of apprenticeship, an organization gives an exam that must be passed to be eligible for membership. Let

(randomly chosen apprentice passes). The organization wishes an exam that most but not all should be able to pass, so it decides that is desirable. For a particular exam, the relevant hypotheses are versus the alternative . Suppose ten people take the exam, and let the number who pass.

a. Does the lower-tailed region 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 as a function of p for this test.

Is this desirable