A manufacturer produces pistons rings for automobile engine. It is known that the ring is approximately normally distributed as well as has standard deviation of s = 0.001 mm. A random sample of 15 rings has mean diameter of mm.
(a) Using the proper 99% confidence interval, state and test the hypothesis that the mean piston ring diameter is 74.035 mm.
(b) What is the minimum level of significance to reject the null hypothesis?
(c) What sample size is required to detect a true mean diameter of 74.03 with a probability of at least 0.95?