A study of 10 different weight loss programs involved 200 subjects. Each of the

Question

A study of 10 different weight loss programs involved 200 subjects. Each of the 10 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 10 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 10 programs at the significance level of 0.05? Explain.

Mean Square (MS) Sum of Squares Degrees of Freedom Source of Variation (sS) (dp Factor 53.6 way Error (Within) N/A Total 553.05 199

Explanation / Answer

here SSE =553.05-53.6=499.45

df (factor) =programme-1=10-1=9

df(error)=199-9=190

MS(factor) =SS/df =53.6/9=5.96

MS(error)=SS/df =499.45/190=2.63

hence test statistic F=MS(factor)/MS(error)=2.27

c) for above test statistic and (9,190) df p value =0.0197

d) as p vlaue is less than 0.05 level wehave sufficient evidence to conldue that the mean weight loss is not the same for the 10 programs at the significance level of 0.05

Source SS df MS F Factor 53.6 9 5.96 2.27 error 499.45 190 2.63 total 553.05 199

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