A study of 10 different weight loss programs involved 500 subjects. Each of the

Question

A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs had 50 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.

Source of variation Sum of Squares Degrees of freedom Mean Square Factor(between) 27.82 Error(Within) 95 Total 985.07 499 N/A

Explanation / Answer

a)

please find table

b) test stat =MSA/MSE =3.09/0.194=15.94

c) for 9 df in numerator and 490 df in denominator for above test stat F; p value=0.0000

d)as p value is less then 0.05 level, we reject null hypothesis, and have sufficient evidence to reject the claim that the mean weight loss is the same for the 10 programs at the significance level of 0.05

Source of variation Sum of Squares Degrees of freedom Mean Square Factor(between) 27.82 10-1=9 27.82/9=3.09 Error(Within) 95 499-9=490 95/490=0.194 Total 985.07 499

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