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Constructing and Understanding the ANOVA

Martin Motors has in stock three cars of the same make and model. The president would like to compare the gas consumption of the three cars (labeled car A, car B, and car C) using four different types of gasoline. For each trial, a gallon of gasoline was added to an empty tank, and the car was driven until it ran out of gas. The following table shows the number of miles driven in each trial.

Distance (miles)
Types of Gasoline Car A Car B Car C
Regular 22.4 20.8 21.5
Super regular 17.0 19.4 20.7
Unleaded 19.2 20.2 21.2
Premium unleaded 20.3 18.6 20.4

Using the .05 level of significance:

Is there a difference among types of gasoline?
Is there a difference in the cars?

Solution Preview

Let us take the hypothesis that
a) There is no difference among types of Gasoline and
b) There is no difference in the cars..

Types of
gasoline Cars Total
Car A Car B Car C
Regular 22.4 20.8 21.5 64.7
Super Regular 17.0 19.4 20.7 57.1
Unleaded 19.2 20.2 21.2 60.6
Premium Unleaded 20.3 18.6 20.4 59.3
Total 78.9 79 83.8 241.7 = T

19.725 19.750 20.950

Correction Factor =

Total Sum of squares =


= 4890.83 - 4868.24 = 22.59

Sum of squares between columns ...

Solution Summary

The solution constructs an ANOVA table for Martin Motors. The difference among the gasoline and car types are given.