Question

A medical researcher wishes to try three different techniques to lower blood pressure of patients with high blood pressure. 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 blood pressure is recorded. Test the claim that there is no difference among the means. Use α = 0.05. Resource: The One-Way ANOVA Group 1: 11,12,13,15,9,8 Group 2: 8,2,3,5,4,0 Group 3: 6,12,4,8,9,4

Answer 1

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

One-way ANOVA

Method

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor	Levels	Values
Factor	3	Group 1, Group 2, Group 3

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	2	176.8	88.389	11.09	0.001
Error	15	119.5	7.967
Total	17	296.3

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
2.82253	59.67%	54.29%	41.92%

Means

Factor	N	Mean	StDev	95% CI
Group 1	6	11.33	2.58	(8.88, 13.79)
Group 2	6	3.67	2.73	(1.21, 6.12)
Group 3	6	7.17	3.13	(4.71, 9.62)

Pooled StDev = 2.82253

Here the p-value is smaller than the level of significance. i.e .

Therefore we have sufficient evidence to reject the null hypothesis at 5% level of significance . so Ho is rejected.

Hence There is a significant difference between the blood pressure by giving medication, exercise program and assign diet program.