It is suspected that using premium gasoline rather than regular will increase the mileage for automobiles with a particular engine design. Sixteen cars are used in a randomized experiment. Eight are randomly chosen to be tested with regular gasoline, while the other eight are tested with premium gasoline. The results, in mpg, are as follows:

a. Under the null hypothesis that each car would get the same mileage with either type of gasoline, how many different outcomes are possible for this experiment?

b. Let R and P denote the sample mean mileages for the regular and premium groups, respectively. Compute R and P.

c. Perform a randomization test to determine whether it can be concluded that premium gasoline tends to increase mileage. Use the test statistic P??R. Generate at least 1000 random outcomes, and estimate the P-value.

d. Use the Student??s t test described in Section 6.7 to test the null hypothesis that the mean mileage using regular is greater than or equal to the mean mileage for premium. Is this result reliable? Explain?

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Regular: 29.1 27.1 30.8 17.3 27.6 16.3 28.4 30.2 Premium: 28.3 32.0 27.4 35.3 29.9 35.6 30.9 29.7