Looking for the answer for 9-30 which is based off of 9-29 A quality-control ins

Question

Looking for the answer for 9-30 which is based off of 9-29

A quality-control inspector is testing a batch of printed circuit boards to see whether they are capable of performing in a high temperature environment. He knows that the boards that will survive will pass all five of the tests with probability 98%. They will pass at least four tests with probability 99%, and they always pass at least three. On the other hand, the boards that will not survive sometimes pass the tests as well. In fact, 3% pass all five tests, and another 20% pass exactly four. The rest pass at most three tests. The inspector decides that if a board passes all five tests, he will classify it as "good." Otherwise, he'll classify it as "bad." (a) What does a type I error mean in this context? (b) What is the probability of a type I error? (c) What does a type II error mean here? (d) What is the probability of a type II error? In the quality-control example of Exercise 9-29, the manager says that the probability of a type I error is too large and that it must be no larger than 0.01. (a) How does this change the rule for deciding whether a board is "good"? (b) How does this affect the type II error? (c) Do you think this reduction in type I error is justified? Explain briefly.

Explanation / Answer

Solution:

a) type I error : It means rejecting a good board (classifying it as a bad board).

b) type I Probability =1-.98=.02

c) type II error: Failing to reject a board when it is in fact bad (classifying it as a good board)

d) type II Probability = 0.03

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