A car company is attempting to develop a reasonably priced gasoline that will deliverimproved gasoline mileages....

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A car company is attempting to develop a reasonably pricedgasoline that will deliverimproved gasoline mileages. As part ofits development process, the company would like to compare theeffects of three types of gasoline (A, B and C) on gasolinemileage. For testing purposes, the company will compare the effectsof gasoline types A, B and C on the gasoline mileage obtained by apopular mid-size car. 10 cars are randomly selected to be assignedtoeach gasoline type (A, B and C), i.e.,nA =nB = nC = 10. Thegasoline mileage for eachtest drive is measured.It is found thatthe gasoline mileage sample means of the three groups are 34.92,36.56 and 33.98. The ANOVA table for the three-group model issummarized as following.
Sum sq Df MeanSq F Stat pvalue
Betweengroup 18.0493 2 9.0247 14.3097 0.0001
Withingroup 17.0280 27 0.6307
Total 35.0773 29
Let ?A, ?B, and ?C be the mean mileages of gasoline types A, B,and, C respectively. Carry out an overal test to determine if thereis significant difference among ?A, ?B, and ?C at the sinificancelevel of 1%.

	Sum sq	Df	MeanSq	F Stat	pvalue
Betweengroup	18.0493	2	9.0247	14.3097	0.0001
Withingroup	17.0280	27	0.6307
Total	35.0773	29

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