A consumer group is testing a manufacturer’s claim that a new car model will travel at least 30 miles per gallon of gasoline. Assume that &#55349;&#56379;0:&#55349;&#57095;=30 and &#55349;&#56379;&#55349;&#56398;:&#55349;&#57095;

Question

A consumer group is testing a manufacturer’s claim that a new car model will travel at least 30 miles per gallon of gasoline. Assume that &#55349;&#56379;0:&#55349;&#57095;=30 and &#55349;&#56379;&#55349;&#56398;:&#55349;&#57095;<30, and that the population standard deviation &#55349;&#57102; is known and is equal to 3.2 miles per gallon. An SRS of 40 cars will be used for this test, with a level of significance of &#55349;&#57084;=0.01. 
Compute the power of this test assuming a proposed alternative value for &#55349;&#57095; of 27.5 miles per gallon (i.e. assuming &#55349;&#57095;&#55349;&#56398;=27.5).