Question

A consumer advocate examines whether the longevity of car batteries (measured in years) is affected by the brand name (factor A) and whether or not the car is kept in a garage (factor B). Interaction is suspected. The results are shown in the accompanying table.

Garage	Brand	Years
Yes	A	7
Yes	A	8
Yes	A	8
No	A	7
No	A	6
No	A	6
Yes	B	7
Yes	B	7
Yes	B	6
No	B	5
No	B	4
No	B	4
Yes	C	8
Yes	C	8
Yes	C	8
No	C	6
No	C	6
No	C	6

	ANOVA Source of Variation Df Sum Sq Mean Sq F value Pr(>F) Garage Brand Garage:Brand Residuals

a-2. At the 5% significance level, Is there interaction between the brand name and whether a car is garaged?

• Yes, since the p-value for interaction is less than the significance level.

• Yes, since the p-value for interaction is greater than the significance level.

• No, since the p-value for interaction is greater than the significance level.

• No, since the p-value for interaction is less than the significance level.

Answer 1

To test whether there is any interaction between the brand name and whether a car is garaged,

i.e. H₀ : There is no interaction between the brand name and whether a car is garaged

against

H₁ : There is interaction between the brand name and whether a car is garaged

The value of the test statistic F = 1.75

and p-value = 0.215

Since p-value > 0.05, so we fail to reject H₀ and we can conclude that there is no significant interaction between the brand name and whether a car is garaged.

ans-> No, since the p-value for interaction is greater than the significance level.