Question

In: Statistics and Probability

A medical researcher wishes to try three different techniques to lower the blood pressure of patients...

A medical researcher wishes to try three different techniques to lower the 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. Find the test statistic F to test the claim that there is no difference between the means.

Group 1 Group 2 Group 3

11 8 6

12 2 12

9 3 4

15 5 8

13 4    9

8 0 4

11.33 3.67 7.17 (Mean)

2.58 2.73 3.13(SD)

1. Identify the null hypothesis

2. Identify the alternative hypothesis

3. Determine the F value of the F test statistics

4. Identify the P-value

5. State the conclusion of the null hypothesis

6. State the final conclusion that addresses the original claim

7. Write the result in APA format.

Solutions

Expert Solution

Group 1 Group 2 Group 3 Total
Sum 68 22 43 133
Count 6 6 6 18
Mean, Sum/n 11.33333 3.666667 7.166667
Standard deviation 2.581989 2.73252 3.125167

Null and Alternative Hypothesis:

Ho: µ1 = µ2 = µ3

H1: At least one mean is different.

Number of treatment, k = 3

Total sample Size, N = 18

df(between) = k-1 = 2

df(within) = N-k = 15

df(total) = N-1 = 17

SS(between) = (x̅1)²*n1 + (x̅2)²*n2 + (x̅3)²*n3 - (Grand Mean)²*N = 176.7778

SS(within) = (n1-1)*s1² + (n2-1)*s2² + (n3-1)*s3² = 119.5

SS(total) = SS(between) + SS(within) = 296.2778

MS(between) = SS(between)/df(between) = 88.3889

MS(within) = SS(within)/df(within) = 7.9667

Test statistic:

F = MS(between)/MS(within) = 11.0948

p-value = F.DIST.RT(11.0948, 2, 15) = 0.0011

ANOVA
Source of Variation SS df MS F P-value
Between Groups 176.7778 2 88.3889 11.0948 0.0011
Within Groups 119.5000 15 7.9667
Total 296.2778 17

Decision:

P-value < α, Reject the null hypothesis.

There is enough evidence to reject the claim that there is no difference between the means.


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