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See attached file for clarity.

Analysis of Variance

My brother is interested in buying a car, but knows very little about them. He has gone to a used car dealership and looked at cars. His one criteria is that the car gets good gas mileage. The car salesman tells him that the number of cylinders in a car has nothing to do with gas mileage; thus, it makes no difference whether he gets a 4, 6, or 8 cylinder car, since they all get similar gas mileage. My brother comes to me and asks my opinion. I do a little research and find the miles per gallon for city driving for a random sample of 4, 6, and 8 cylinder cars.

The results are as follows:
Four Cylinder City MPG Six Cylinder City MPG Eight Cylinder City MPG
22 18 17
20 21 17
24 21 17
22 18 18
26 19 18
24 18 17
24 17 17
25 22
26 27
23 22
24 22
30 20

In order to check whether there is a difference in City MPG among the three different types of cars, I run a oneway ANOVA (using Statdisk, of course!) and get the following results:

Source: DF: SS: MS: Test Stat, F: Critical F: P-Value:
Treatment: 2 216.529762 108.264881 19.828077 3.327651 0.000004
Error: 29 158.345238 5.460181
Total: 31 374.875

Should my brother believe the car salesman? Is there really no difference among the three types of cylinder cars? Or is this a case of not being able to believe a used car salesman? What decision should my brother make, if he wants to get the best city gas mileage (MPG)?


Solution Preview

See attached file.

You are testing if the three groups of cars get statistically significantly different gas mileage.

Null hypothesis: each of the three groups of cars has the same average MPG
Alternative hypothesis: at least one of the groups ...