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?
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