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.

	Brand Name of Battery
Kept in Garage?	A	B	C
Yes	6, 8, 8	5, 5, 5	7, 9, 10
No	7, 6, 6	5, 5, 5	7, 7, 7

a-1. Construct an ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "SS", "MS" to 4 decimal places and "F", "p-value" to 3 decimal places.)

Source of variation	SS	df	MS	F	p-value
Sample
Columns
Interaction
Within
Total

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.

b. At the 5% significance level, can you conclude that the average battery lives differ by brand name?

• No since the p-value for brand name is less than the significance level.
• Yes since the p-value for brand name is less than the significance level.
• No since the p-value for brand name is less than the significance level.
• No since the p-value for brand name is greater than the significance level.

c. At the 5% significance level, can you conclude that the average battery lives differ depending on whether a car is garaged?

• Yes since the p-value for garage is greater than the significance level.
• Yes since the p-value for garage is less than the significance level.
• No since the p-value for garage is less than the significance level.
• No since the p-value for garage is less than the significance level.

Answer 1

Answer Date: 31/07/2020 a-1) The two-way analysis of variance is, By using Excel software, find two-way analysis of variance with the help of following steps: 1) Import the data. 2) Choose ANOVA: Two Factor With Replication from Data Analysis in Data menu. 3) Select Labels. 4) Choose Input Range and enter Rows per sample (3). 5) Choose Output Range and enter Alpha. 6) Click Ok.

The two-way analysis of variance table Excel output is, df ANOVA Source of Variation Sample (Garage) Columns (Brands) Interaction Within Total SS 3.5556 24.7778 2.1111 8.0000 38.4444 1 2. 2 12 17 MS 3.5556 12.3889 1.0556 0.6667 F 5.333 18.583 1.583 P-value 0.040 0.0002 0.245 a-2) From Excel output in (a-1), the p-value is higher than 0.05 which is 0.245, so the null hypothesis is not rejected at 5% level of significance. It cannot infer that there is an interaction between the brand name and whether a car is garaged. The result is not statistically significant. The correct option is 3 b)

From Excel output in (a-1), the p-value is less than 0.05 which is 0.0002, so the null hypothesis is rejected at 5% level of significance. It can infer that the average battery lives differ by brand name. The result is statistically significant. The correct option is 2 From Excel output in (a-1), the p-value is less than 0.05 which is 0.040, so the null hypothesis is rejected at 5% level of significance. It can infer that the average battery lives differ depending on whether a car is garaged. The result is statistically significant. The correct option is 2.