A manufacturer produces crankshaft for an automobile engine. The crankshafts wear after 100,000 mile (0.0001 inch) is of interest because it is likely to have an impact on warranty claims. A random sample of n = 12 shafts is tested and = 2.75. It is known that = 0.6 and that wear is normally distributed. (a) Test H0: = 3 versus H1: 3 using = 0.05. (b) What is the power of the test if = 3.15? (c) What sample size would be required to detect a true mean of 3.5 if we wanted the power to be at least 0.95?