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):

Source of Variation

Sum of Squares

(SS)

Degrees of Freedom (df)

Mean Square

(MS)

Factor

(Between)

53.6

Error

(Within)

Total

553.05

199

N/A

                        (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.

Source of Variation

Sum of Squares

(SS)

Degrees of Freedom (df)

Mean Square

(MS)

Factor

(Between)

53.6

Error

(Within)

Total

553.05

199

N/A

Explanation / Answer

here from above information below is one way ANOVA table:

b)  test statistic =MS(factor)/MS(error)=5.96/2.63=2.27

c) for (9,190) degree of freedom and above test statistic p value =0.0197

d) as p value is less than 0.05 level we reject null and conclude that ean weight loss is the different for at least one programs at the significance level of 0.05

source SS df MS factor 53.6 9 5.96 error 499.45 190 2.63 total 553.05 199

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