Can you do 9.30? 9-29. A quality-control inspector is testing a batch of printed

Question

Can you do 9.30?

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?

9-30. 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.

9-29. A quality-control inspector is testing a batch of printed circuit boards to see whether they are capable of f the tests that the boards that will survive will pass all five o 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? 9-30. 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 (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

9.29) a) if we want to test the following hypothisis in this context

H: the board is good vs K: the board is not good/bad

by type -I error we mean that rejection of true H...if a the board is really good but reject it by saying thequality of it is poor or bad....

b) P(type one error)=P(rejection of true H)..in our problem 98% passes exacly 5 test..that those 98% are good in quality....if we reject a good one then it should be type -1 error.the probability is 1-.98=.02

c) type -II error means acceptance of false H...in this context if a board is not good enough but we are interested to accept the board as a good one..then it will be type -II eror..

d) P(type II error)=P(acceptence of false H )=P(the board is not good but still we accept it)=.03

9.30) a) the manager says that the type -I error is no loger than .01 that is P(type -I error )<=.01 under null the expectation of the test fuction (rule ) is atmost .01

b) if we want to decrease type -I error then Type II error is incresed . The main thing is that performance of the test is depend upon this two probability ..we always try to minimize this two error..but simultaneous minimization is not possible ..as an example when we minimize the type I error as aresult s ina shrinkage of the critical region subsequentially acceptance region expands .so as a resut probability of the type II error is increased..

c) reduction in type II error is justified as in practical rejection of true H (null) considered as more serious than acceptence of false H..other thing if our type I error is .01 then we can say that if we conducted the test 100 times atmost 1 time true H is rejected so thats why we always try to keeep type I error low...

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.