A car manufacturer claims that its vehicles average at least 24 miles per gallon, with a population standard deviation of σ=3. We take a sample of n=16 cars to test fuel efficiency, and with to performance a one-sided hypothesis test of the manufacturer's claim at a level of α=.025.
a. What is the critical value for the sample mean?
b. Suppose the answer to part a is 23 (it is not, but assume it is to do part b). If the true value of efficiency in the population is 22.5, what is the power of this hypothesis test?