11.72 The EPA wants to model the gas mileage rating Y of automobiles as a function of their engine size x. A quadratic model Y = b0 + b1x + b2x2 R2

+ b4x1x2 + b5x1x3 E(Y ) = b0 + b1x1 + b2x2 + b3x3

(x2 = 0, x3 = 1)

is proposed. A sample of 50 engines of varying sizes is selected, and the miles per gallon rating of each is determined. The least-squares model is The size x of the engine is measured in hundreds of cubic inches. Also, and a Sketch this model between and .
b Is there evidence that the quadratic term in the model is contributing to the prediction of the miles per gallon rating Y? Use .
c Use the model to estimate the mean miles per gallon rating for all cars with 350-cubicinch engines .
d Suppose a 95% confidence interval for the quantity estimated in part

(c) is (17.2, 18.4).
Interpret this interval.
(x = 3.5)
a = 0.05 x = 1 x = 4 R2 = 0.93.
sb N 2 = 0.0037 yN = 51.3 - 10.1x + 0.15x 2 e Suppose you purchase an automobile with a 350-cubic-inch engine and determine that the miles per gallon rating is 14.7. Is the fact that this value lies outside the confidence interval given in part

(d) surprising? Explain.