A quality - control inspector is testing a batch of printed circuit boards to se
ID: 3241631 • Letter: A
Question
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, hell 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?Explanation / Answer
Solution:
a. Type 1 error means that a good sample is rejected.
here, it means that a circuit board which will survive is not able to pass all 5 tests and is therefore labelled as bad.
b. Since only 98% of circuit board which will survive are able to pass all 5 tests, so, the probaility of type 1 error is 2%.
c. Type 2 error means that a bad sample is accepted.
here, it means that a circuit board which will not survive is able to pass all 5 tests and is therefore labelled as good.
b. Since only 3% of circuit board which will not survive are able to pass all 5 tests, so, the probaility of type 2 error is 3%.