Question

3. A semiconductor manufacturer produces controller used in automobile engine applications. The customer requires that the process fallout or fraction defective at a critical manufacturing step not exceed 0.05 and that the manufacturer demonstrate process capability at this level of quality using a 0.05. The semiconductor manufacturer takes a random sample of 200 devices and finds that four of them are defective. Can you check the (3 points) manufacturer claim?

Answer 1

Data:    

n = 200   

p = 0.05   

p' = 4/200 = 0.02   

Hypotheses:   

Ho: p ≤ 0.05   

Ha: p > 0.05   

Decision Rule:   

α = 0.05   

Critical z- score = 1.644853627

Reject Ho if z > 1.644853627

Test Statistic:   

SE = √{(p (1 - p)/n} = √(0.05 * (1 - 0.05)/√200) = 0.015411035

z = (p' - p)/SE = (0.02 - 0.05)/0.0154110350074224 = -1.946657054

p- value = 0.9742121   

Decision (in terms of the hypotheses):

Since -1.946657 < 1.644853627 we fail to reject Ho

Conclusion (in terms of the problem):

There is no sufficient evidence that the fraction defective is more than 0.05. The customer need not worry.

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