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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Description: 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 populatio

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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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