Question

1. A researcher is interested in studying the effect that the amount of fat in the diet and amount of exercise has on the mental acuity of middle-aged women. The researcher used three different treatment levels for the diet and two levels for the exercise. The results of the acuity test for the subjects in the different treatment levels are shown below.

	Diet
Exercise	<30% fat	30% - 60% fat	>60% fat
<60 minutes	4	3	2
	4	1	2
	2	2	2
	4	2	2
	3	3	1
60 minutes	6	8	5
or more	5	8	7
	4	7	5
	4	8	5
	5	6	6

Answer 1

The results are:

Source	SS	df	MS	F	p-value
Exercise	90.13	1	90.133	135.20	2.39E-11
Diet	6.20	2	3.100	4.65	.0196
Interaction	18.47	2	9.233	13.85	.0001
Error	16.00	24	0.667
Total	130.80	29

The hypothesis being tested is:

H₀: There is no interaction effect of the amount of fat in the diet and amount of exercise on the mental acuity of middle-aged women

H_a: There is an interaction effect of the amount of fat in the diet and amount of exercise on the mental acuity of middle-aged women

The p-value from the output is 0.0001.

Since the p-value (0.0001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is an interaction effect of the amount of fat in the diet and amount of exercise on the mental acuity of middle-aged women.