Homework SourseThe price drivers pay for gasoline often varies a great deal
The price drivers pay for gasoline often varies a great deal across regions throughout the United States. The following data show the price per gallon for regular gasoline for a random sample of gasoline service stations for three major brands of gasoline (Shell, BP, and Marathon) located in eleven metropolitan areas across the upper Midwest region.
Use = .05 to test for any significant difference in the mean price of gasoline for the three brands. Round SS to 6 decimals, MS to 7 decimals, F to 2 decimals and p to 3 decimals, if necessary.
The p-value is
Less than 0.05
Between 0.5 and 0.125
Between 0.25 and 0.05
Between 0.05 and 0.10
Greater than 0.05
| Metropolitan Area | Shell | BP | Marathon |
| Akron, OH | 3.77 | 3.83 | 3.78 |
| Cincinnati, OH | 3.72 | 3.83 | 3.87 |
| Cleveland, OH | 3.87 | 3.85 | 3.89 |
| Columbus, OH | 3.76 | 3.77 | 3.79 |
| Ft. Wayne, IN | 3.83 | 3.84 | 3.87 |
| Indianpolis, IN | 3.85 | 3.84 | 3.87 |
| Lansing, MI | 3.93 | 4.04 | 3.99 |
| Lexington, KY | 3.79 | 3.78 | 3.79 |
| Louisville, KY | 3.78 | 3.84 | 3.79 |
| Muncie, IN | 3.81 | 3.84 | 3.83 |
| Toledo, OH | 3.69 | 3.83 | 3.86 |
Solution
H0: There is no significant difference in the mean price of gasoline for the three brands
H1: There is significant difference in the mean price of gasoline for the three brands
The anova table is calculated as
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Two-way ANOVA: Price per gallon versus Metropolitan Area, Major Brands
Source DF SS MS F P
Metropolitan Area 10 0.108006 0.0108006 8.30 0.000
Major Brands 2 0.015836 0.0079182 6.08 0.009
Error 20 0.026030 0.0013015
Total 32 0.149873
S = 0.03608 R-Sq = 82.63% R-Sq(adj) = 72.21%
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As per table the p-value of major brans is less than 0.05. So we reject H0.
That is there is significant difference in the mean price of gasoline for the three brands
