A manufacturer produces crankshafts for an automobile engine. The wear of the crankshaft after 100,000 miles (0.0001 inch) is of interest because it is likely to have an impact on warranty claims. A random sample of n = 15 shafts is tested and 2.78. It is known that σ = 0.9 and that wear is normally distributed.
(a) Test H0: μ = 3 versus Ho: μ  3 using a = 0.05.
(b) What is the power of this test if μ = 3.25?
(c) What sample size would be required to detect a true mean of 3.75 if we wanted the power to be at least 0.9?