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The fraction of defective integrated circuits produced in a photolithography process is being studied. A random...

  1. The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 circuits is tested, revealing 18 defectives.

(a) Use the data to test the hypothesis that the proportion is not 0.04. Use α = 0.05.

(b) Find the P-value for the test.

(c) Find a 95% two-sided traditional CI on the proportion defective.

(d) Use the CI found in part (c) to test the hypothesis.

(e) Suppose that the fraction defective is actually p = 0.05. What is the β-error for this test?

(f) Suppose that the manufacturer is willing to accept a β-error of 0.10 if the true value of p is 0.05. With 0.05, what sample size would be required?

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