A manufacturer produces pistons rings for an automobile engine. It is known that the ring is approximately normally distributed and has standard deviation of σ = 0.001 mm. A random sample of 15 rings has a mean diameter of x-bar 74.036 mm.
(a) Using a level of significance of 0.01, state and test the hypothesis that the mean piston ring diameter is 74.035 mm. Draw conclusions.
(b) What is the minimum level of significance to reject the null hypothesis?
(c) What are the lower and upper specifications limits (a, b) such that only 2.5% of the pistons ring would exceed the limits.
(d) What is the power of the test if the true mean shifts by one standard deviation?