A new process for producing silicon wafers for integrated circuits is supposed to reduce the proportion of defectives to 10%. A sample of 250 wafers will be tested. Let X represent the number of defectives in the sample. Let p represent the population proportion of defectives produced by the new process. A test will be made of H₀ : p ≥ 0.10 versus H₁ : p < 0.10. Assume the true value of p is actually 0.06.

a. It is decided to reject H₀ if X ≤ 18. Find the level of this test.

b. It is decided to reject H₀ if X ≤ 18. Find the power of this test.

c. Should you use the same standard deviation for X to compute both the power and the level? Explain.

d. How many wafers should be sampled so that the power is 0.90 if the test is made at the 5% level?