Amanufacturer 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 x - = 2.78. it is known that sigma = 0.9 and that wear is normally distributed. a. test h0: mu = 3 versus ? 1: mu 3 using alpha = 0.05. b. what is the power of this test if mu, = 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?