Question

CH13 Q10

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 Batter Kept in Garage? Yes No 7, 8, 6 7, 6, 7 9, 7, 10 7, 7, 6 5, 4, 5 6, 6, 6 he 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.) Answer is not complete ANOVA Source of Variation Sample Columns df MS p-value Within Total 0.0000

Answer 1

Here we have data:

	YES	NO
A	7	7
A	8	7
A	6	6
B	7	5
B	6	4
B	7	5
C	9	6
C	7	6
C	10	6

Here calculate by Excel

Excel output:

Anova: Two-Factor With Replication
SUMMARY	YES	NO	Total
A
Count	3	3	6
Sum	21	20	41
Average	7	6.66666667	6.833333
Variance	1	0.33333333	0.566667
B
Count	3	3	6
Sum	20	14	34
Average	6.6666667	4.66666667	5.666667
Variance	0.3333333	0.33333333	1.466667
C
Count	3	3	6
Sum	26	18	44
Average	8.6666667	6	7.333333
Variance	2.3333333	0	3.066667
Total
Count	9	9
Sum	67	52
Average	7.4444444	5.77777778
Variance	1.7777778	0.94444444
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	8.7778	2	4.3889	6.077	0.015	3.885
Columns	12.5	1	12.5	17.308	0.001	4.747
Interaction	4.3333	2	2.1667	3.000	0.088	3.885
Within	8.6667	12	0.7222
Total	34.2778	17