A researcher wishes to see whether the type of gasoline used and the type of automobile driven have any effect on gasoline consumption. Two types of gasoline, regular and high-octane, will be used, and two types of automobiles, two-wheel- and all-wheeldrive, will be used in each group. There will be two automobiles in each group, for a total of eight automobiles used. Using a two-way analysis of variance, determine if there is an interactive effect, an effect due to the type of gasoline used, and an effect due to the type of vehicle driven.
The data (in miles per gallon) are shown here, and the summary table is given in Table \(12-6\).

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Gas Two-wheel-drive Type of automobile All-wheel-drive Regular 26.7 28.6 25.2 29.3 High-octane 32.3 26.1 32.8 24.2 TABLE 12-6 ANOVA Summary Table for Example 12-6 Source Sum of squares Gasoline (A) 3.920 Automobile (B) 9.680 Interaction (AxB) 54.080 Within (error) 3.300 Total 70.980 d.f. Mean square F