Martin Motors has in stock three cars of the same make and model. The president

Question

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 A, B, and C using four different types of gasoline. For each trial, a gallon of gasoline was addd 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)
Type 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 a .05 significance level, is there a difference among the types of gasoline?

Is there a difference in the cars?

Explanation / Answer

We use two-way ANOVA to analyze the data. The output is as follows: Anova: Two-Factor Without Replication SUMMARY Count Sum Average Variance Regular 3 64.7 21.56666667 0.643333333 Super Regular 3 57.1 19.03333333 3.523333333 Unleaded 3 60.6 20.2 1 Premium Unleaded 3 59.3 19.76666667 1.023333333 Car A 4 78.9 19.725 5.0625 Car B 4 79 19.75 0.916666667 Car C 4 83.8 20.95 0.243333333 ANOVA Source of Variation SS df MS F P-value F crit Rows 10.20916667 3 3.403055556 2.413990148 0.164988317 4.757062664 Columns 3.921666667 2 1.960833333 1.390935961 0.318927857 5.14325285 Error 8.458333333 6 1 .409722222 Total 22.58916667 11 Using the .05 level of significance: a. Is there a difference among types of gasoline? No. b. Is there a difference in the cars? No.

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