Consider a manufacturing company that produces shafts for an airplane engine. Studying the shaft wear after 1,000 hours of flight is of interest, because the wear can affect the airplane performance. A random sample of 10 shafts is tested, and the sample mean wear is found to be 2.63. It is known that=0.7 and that the wear is normally distributed. To answer the questions below, use=0.03.

(a) Is there enough evidence to conclude that the shaft wear is smaller than 3.0? Use an appropriate hypothesis test and state your conclusions.

(b) For a type II error probability, the corresponding statistical power is equal to1. What is the power of the test in part (a) if=3.20?

(c) Explain how a type I and a type II error could occur in the test from part (a).