4. (20 points) Does the weight of a vehicle affect the gas mileage? The followin

Question

4. (20 points) Does the weight of a vehicle affect the gas mileage? The following random sample was collected where x- weight of a vehicle in hundreds of pounds and y miles per gallon. x (lb hundreds) 263 29 39 20 y (mpg) 22.0 16.1 18.8 5.723.4 a) The linear correlation is determined to be r 9701. Conduct an appropr hypothesis test to determine if the weight and mpg of a vehicle are correlated. The regression equation is determined to be: mpg 32.5-0.45x weight. (b) What is the predict mpg for a car weighing 24 (hundred) pounds? (c) What is the predicted weight for a car the gets 22 mpg? Page 5

Explanation / Answer

A)

T=r*sqrt((n-2)/(1-r^2))

=-0.9701*sqrt(3/(1-0.9701^2))

=-6.29

Since t is much less than critical value

We reject the null hypothesis

There is significant correlation.

B)y^=32.5-0.45*weight

=32.5-0.45*24

=21.7

C)22=32.5-0.45*weight

Weight=10.5/0.45

=23.33333

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