An automotive engineer wanted to determine whether the octane of gasoline used in a car increases gas mileage. Recognizing that car and driver are variables that affect gas mileage, he selected six different brands of car and assigned a driver to each car, so he blocked by car type and driver. For each car (and driver), the researcher randomly selected a number from 1 to 3, with 1 representing 87-octane gasoline, 2 representing 89-octane gasoline, and 3 representing 92-octane gasoline. Then 5 gallons of the gasoline selected was placed in the car. The car was driven around a closed track at 40 miles per hour until the car ran out of gas. The number of miles driven was recorded and then divided by 5 to obtain the miles per gallon. He obtained the following results:

(a) Normal probability plots for each treatment indicate that the requirement of normality is satisfied. Verify that the requirement of equal population variances for each treatment is satisfied.
(b) Explain the role blocking plays in reducing the variability of gas mileage.
(c) Is there sufficient evidence that the mean miles per gallon are different among the three octane levels at the a = 0.05 level of significance?
(d) If the null hypothesis from part (c) was rejected, use Tukey's test to determine which pairwise means differ using a familywise error rate of a = 0.05.
(e) Based on your results for part (d), what do you conclude?

87 Octane 89 Octane 92 Octane Chevrolet Impala 28.3 28.4 28.7 Chrysler 300M 26.9 27.2 27.1 Ford Taurus 26.4 26.1 26.8 26.4 Lincoln LS 26.1 27.3 Toyota Camry 28.4 28.9 29.1 Volvo S60 25.3 25.1 25.8