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)

Error

(Within)

Total

653.05

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)

65.4

Error

(Within)

Total

653.05

199

N/A

Explanation / Answer

a) The ANOVA table is

Df for Factor = 10-1 = 9
Df for Error = 199-9 = 190
Sum of Square of Error = 653.05 - 65.4 = 587.65
Mean Square of Factor = 65.4/9 = 7.2667
Mean Square of Error = 587.65/190 = 3.092894

b)
Test Statistic F = 7.2667 / 3.09289 = 2.34947

c)P-value = 0.015524931

Here P - value = 0.015525 < alpha 0.05, So we reject H0

d) We conclude that there is insufficient evidence to support the claim that the mean weight loss is the same for the 10 programs at the significance level of 0.05.

i.e.There is the mean weight loss is not same for the 10 programs

Source df Sum of square mean Square F Factor (Between) 9 65.4 7.266666667 2.349471 Error (Within) 190 587.65 3.092894737 Total 199 653.05

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