Question

1. Each of three cars is driven with each of four different brands of gasoline. The number of miles per gallon driven for each of the ab = (3)(4) = 12 different combinations is recorded below.

Car	1	2	3	4
1	26	28	31	31
2	24	25	28	27
3	25	25	28	26

1. Test the hypothesis that we can expect the same mileage for each of these four brands of gasoline at α = 0.01.
2. Test the hypothesis that we can expect the same mileage for each of these three models of car at α = 0.01.
3. Is there any evidence of interaction between gasoline brands and type of cards in determining mileage driven at α = 0.01?

Answer 1

a)

Using Excel

data -> data analysis -> Anova: Two-Factor Without Replication

Get & Transform Data Queries & Connections Data Types Sort & Filter Data Tools Forecast A9 SUMMARY Anova: Two-Factor Without Replication Input Input Range: ок | SA$1:$E$4 A B C D E 1 Cancel 1 Car 1 2 3 4 Labels Alpha: 0.011 Help 25 25 25 Output options O Qutput Range: 7 Anova: Two-Factor Without Replication New Worksheet Ply: New Workbook SUMMARY Count Sum Average Variance

Anova: Two-Factor Without Replication SUMMARY Count 4 4 4 Sum 116 104 Average Variance 29 6 26 3.333333 26 104 3 78 26 بیا 29 بیا 1 84 28 F ANOVA Source of Variation Rows Columns Error MS 12 10 6 0.666667 P-value Fcrit 18 0.002915 5.143253 15 0.003401 4.757063 Total 58 11

p-value for Gasoline = 0.0034 < alpha

hence we reject the null hypothesis

b)

p-value for car models = 0.0029 < alpha

hence we reject the null hypothesis