題組內容

1.(15%) When a machine that is used to make bolts at a Steel Corporation is working properly, the mean length of these bolts is 2.5 inches. However, from time to time this machine falls out of alignment and produces bolts that have a mean length of cither less than 2.5 inches or more than 2.5 inches. When this happens, the process is stopped and the machine is adjusted. To check whether or not the machine is producing bolts with a mean Jength of 2.5 inches, the quality control department at the company takes a sample of bolts each week and makes a test of bypothesis.

(2)Suppose the null hypothesis stated in that example is false and the true mean length of all bolts produced by the machine at the time of the selection of the sample was 2.498 inches. What is the probability of making a Type II error if a=0.05? What is the power of the test? (8%)