# Question

Octane is a measure of how much the fuel can be compressed before it spontaneously ignites. Some people believe that higher-octane fuels result in better gas mileage for their cars. To test this claim, a researcher randomly selected 11 individuals (and their cars) to participate in the study. Each participant received 10 gallons of gas and drove his or her car on a closed course that simulated both city and highway driving. The number of miles driven until the car ran out of gas was recorded. A coin ﬂip was used to determine whether the car was ﬁlled up with 87-octane or 92-octane fuel ﬁrst, and the driver did not know which type of fuel was in the tank. The results are in the following table:

(a) Why is it important that the matching be done by driver and car?

(b) Why is it important to conduct the study on a closed track?

(c) The norm al probability plots for miles on 87 octane and miles on 92 octane are shown. Are either of these variables normally distributed?

(d) The differences are computed as 92 octane minus 87 octane. The normal probability plot of the differences is shown. Is there reason to believe that the differences are normally distributed? Conclude that the differences can be normally distributed even though the original data are not.

(e) The researchers used MINITAB to determine whether the mileage from 92 octane is greater than the mileage from 87 octane. The results are as follows:

What do you conclude? Why?

(a) Why is it important that the matching be done by driver and car?

(b) Why is it important to conduct the study on a closed track?

(c) The norm al probability plots for miles on 87 octane and miles on 92 octane are shown. Are either of these variables normally distributed?

(d) The differences are computed as 92 octane minus 87 octane. The normal probability plot of the differences is shown. Is there reason to believe that the differences are normally distributed? Conclude that the differences can be normally distributed even though the original data are not.

(e) The researchers used MINITAB to determine whether the mileage from 92 octane is greater than the mileage from 87 octane. The results are as follows:

What do you conclude? Why?

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