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%.
