It Has Been Estimated That The $G$ -Car Obtains a Mean of 40 Miles Per Gallon on Mean

Essay

It has been estimated that the $G$ -car obtains a mean of 40 miles per gallon on the highway, and the company that manufactures the car claims that it exceeds this estimate in highway driving. To support its assertion, the company randomly selects $49 \mathrm { G }$ -cars and records the mileage obtained for each car over a driving course similar to that used to obtain the estimate. The following data resulted: $\bar { x } = 41.5$ miles per gallon, $s = 7$ miles per gallon. Calculate the power of the test if the true value of the mean is 41 miles per gallon. Use a value of $\alpha = .025$ .