Question

Suppose the breaking strength of plastic bags is a Gaussian random variable. Bags from company 1 have a mean strength of 8 kilograms and a variance of 1 kg2 ; Bags from company 2 have a mean strength of 9 kilograms and a variance of 0.5 kg2 . Assume we check the sample mean ?̅ 10 of the breaking strength of 10 bags, and use ?̅ 10 to determine whether a batch of bags comes from company 1 (null hypothesis ?0) or from company 2 (alternative hypothesis ?1). The decision rule is: Accept ?0, if ?̅ 10 ≤ ?; Reject ?0 and accept ?1, if ?̅ 10 > ?. a) (10 pts) Find the threshold ? so that the probability of type I error ? is 5%. b) (5 pts) Calculate ?, the probability of type II error, under this test.

Answer 1