申論題

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.

(1)One such random sample of 49 bolts produced a mean length of 2.49 inches and a standard deviation of 0.021 inches. Using the 5% significance level, can we conclude that the machine needs to be adjusted? (7%)