A study of 8 different weight loss programs involved 160 subjects. Each of the 8

Question

A study of 8 different weight loss programs involved 160 subjects. Each of the 8 programs had 20 subjects in it. The subjects were followed for 12 months. Weight change for each subject was recorded. We want to test the claim that the mean weight loss is the same for the 8 programs. (a) Complete the following ANOVA table with sum of squares, degrees of freedom, and mean square (Show all work): (b) Determine the test statistic. Show all work, writing the correct test statistic, without supporting work, will receive no credit (c) Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit. (d) Is there sufficient evidence to support the claim that the mean weight loss is the same for the 8 programs at the significance level of 0.05? Explain.

Explanation / Answer

(A)

There are 8 groups so degree of freedom of between: df=k-1=7

Degree of freedom of error : df2 = 160 - 8 = 152

Following is the compelted ANOVA:

(b)

The test statistics:

F = 3.390

(c)

The p-value is : 0.0022

(d)

Since p-value is less than 0.05 so we reject the null hypothesis. There is not sufficient evidence to supoort the claim that the mean weight loss is the same for the 8 programs.

SS df MS F Between 27.82 7 27.82/7=3.9743 3.9743/3.3897=1.172 Error 543.05-27.82=515.23 152 515.23/152=3.3897 Total 543.05 159

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