Question

A car company is attempting to develop a reasonably priced gasoline that will deliverimproved gasoline mileages. As part of its development process, the company would like to compare the effects of three types of gasoline (A, B and C) on gasoline mileage. For testing purposes, the company will compare the effects of gasoline types A, B and C on the gasoline mileage obtained by a popular mid-size car. 10 cars are randomly selected to be assigned toeach gasoline type (A, B and C), i.e.,nA =nB = nC = 10. The gasoline mileage for eachtest drive is measured.It is found that the gasoline mileage sample means of the three groups are 34.92, 36.56 and 33.98. The ANOVA table for the three-group model is summarized as following.

	Sum sq	Df	Mean Sq	F Stat	p value
Between group	18.0493	2	9.0247	14.3097	0.0001
Within group	17.0280	27	0.6307
Total	35.0773	29

Let μA, μB, and μC be the mean mileages of gasoline types A, B, and, C respectively. Carry out an overal test to determine if there is significant difference among μA, μB, and μC at the sinificance level of 1%.

Answer 1

Solution:

   We are given that: A car company is attempting to develop a reasonably priced gasoline that will deliverimproved gasoline mileages.
For testing purposes, the company will compare the effects of gasoline types A, B and C on the gasoline mileage obtained by a popular mid-size car. 10 cars are randomly selected to be assigned toeach gasoline type (A, B and C), i.e.,nA =nB = nC = 10.

The ANOVA table for the three-group model is summarized as following.

	Sum sq	Df	Mean Sq	F Stat	p value
Between group	18.0493	2	9.0247	14.3097	0.0001
Within group	17.0280	27	0.6307
Total	35.0773	29

We have to test to determine if there is significant difference among μA, μB, and μC at the sinificance level of 1%.

H0: μ_A = μ_B = μ_C

Vs

H1: At least one of the mean is different from other mean.

Conclusion: Since p value= 0.0001 < 0.01 level of significance we reject null hypothesis: H0: μ_A = μ_B = μ_C and thus we conclude that: there is significant evidence of a difference among μA, μB, and μC at the significance level of 1%.