Question

A medical researcher wishes to try three different techniques to lower cholesterol levels of patients with high cholesterol levels. The subjects are randomly selected and assigned to one of three groups. Group 1 is given medication, Group 2 is given an exercise program, and Group 3 is assigned a diet program. At the end of six weeks, each subject's cholesterol level is recorded. Determine the test statistic F-value to test the hypothesis that there is no difference among the means. Use α = 0.05. (round to the nearest hundredth)

Cholesterol Level

Group 1	Group 2	Group 3
9	8	6
12	3	12
11	2	4
15	5	4
13	4	9
8	0	8

Answer 1

Using Excel. go to Data, select Data Analysis, choose Anova: Single Factor

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	176.78	2	88.39	11.09	0.00	3.68
Within Groups	119.50	15	7.97
Total	296.28	17

H0: μ1 = μ2 = μ3, All means are equal

H1: At least one mean is different from the others

Test statistic = 11.09

p-value = 0.00

Since p-value is less than 0.05, we reject the null hypothesis and conclude that at least one mean is different from the others.