Question

A manufacturer of computer memory chips produces chips in lots of 1000. If nothing has gone wrong in the manufacturing process, at most 5 chips each lot would be defective, but if something does go wrong, there could be far more defective chips. If something goes wrong with a given lot, they discard the entire lot. It would be prohibitively expensive to test every chip in every lot, so they want to make the decision of whether or not to discard a given lot on the basis of the number of defective chips in a simple random sample. They decide they can afford to test 100 chips from each lot. You are hired as their statistician. There is a tradeoff between the cost of eroneously discarding a good lot, and the cost of warranty claims if a bad lot is sold. The next few problems refer to this scenario.

Problem 8 (Continues previous problem.)

a) A type I error occurs if: a) a good lot is discarded, b) a good lot is not discarded, c) a bad lot is discarded, d) a bad lot is not discarded, e) none of the above

b) A type II error occurs if: a) a good lot is discarded, b) a good lot is not discarded, c) a bad lot is discarded, d) a bad lot is not discarded, e) none of the above

Answer 1

Here, below are the null and alternate hypothesis
H0: mu <= 5
Ha: mu > 5

a)
Type I error occurs when a null hypothesis is rejected incorrectly. This means that as a statistician, a person has rejected a good lot and concluded that a lot is defective.

A type I error occurs if a good lot is discarded.

b)
Type II error occurs when one incorrectly fail to reject null hypothesis. This means that as a statistician, a person has failed to reject a bad lot and concluded that a lot is not defective though it is.

A type II error occurs if a bad lot is not discarded