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?

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4 6 2 Driver: Miles on 87 octane Miles orn 92 octane Driver: Miles orn 87 octane Miles on 92 octane 234 257 243 215 114 287 237 238 229 224 119 297 10 315 229 192 204 547 351 241 186 209 562 Probability Plot of 87 Octane Normal 95% CI 9 10. 0.221 p.Va㎞ 0012 AD 臺接 200 -100 100200 300 400 500 600 700 87 Uctane (mileage) Probability Plot of 92 Octane Nor rnal-95% CI 59 263 StDe LI50 15 0 500 P Value 0009 AD 50 20 200 100 100 200 300 400 500 600 700 92 Uctane (mileage) Probability Plot of Difference Nrrnal-95% a Mean 5091 D 1488 AD 034 P-Value 0400 70 50 20 10 -50 0 50 Difference (mileage) Paired T-Test and Cl: 92 Octane, 87 Octane Paired T for 92 Octane -87 Octane StDev SE Mean 263.000 115.041 34.686 32.906 5.09091 14.87585 4.48524 Mean 92 Octane 87 Octane Difference 257.909 109.138 95% lower bound for mean difference: -3.03841 T-Test of mean difference = 0 (vs > 0) : T-Value-1.14 P-Value = 0.141