1) 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?

2) True or False. You MUST write a brief explanation to justify your answer. No explanation=no credit. Partially correct explanation=partial credit.

a. For the events A and B, if (A'∩B') = Ø , then the events are exhaustive. 

b. If a random variable has a Poisson distribution with a mean of 144, then it must also have a standard deviation of 12. 

c. In order to raise the power of a hypothesis test we must lower α. 

d. In a linear regression, all else equal, if SSE decreases, r² decreases