A distributor has received an unlabeled shipment of bait casting

reels from a Korean firm. He usually purchases only two types of

reels, either 7 pound or 9 pound, and he wants to test which

quality he has received. Let H₀ denote the hypothesis that the

mean breaking strength is = 7, where the breaking strength X of

a standard testing length of reel is assumed to have a normal

distribution. Fifteen standard lengths of reel are measured and

tested and the sample mean X is observed to be 8. Find the

probability of a Type I error, if the variance of X is 2 and the

rejection set is X 7.8.