It Has Been Estimated That The $G$ -Car Obtains a Mean of 30 Miles Per Gallon on Mean

It has been estimated that the $G$ -car obtains a mean of 30 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: $\bar { x } = 31.2$ miles per gallon, $s = 7$ miles per gallon. Calculate the value of $\beta$ if the true value of the mean is 32 miles per gallon. Use $\alpha = .025$ .