A study of 8 different weight loss programs involved 160 subjects. Each of the 8
ID: 3221810 • Letter: A
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):
Source of Variation
Sum of Squares
(SS)
Degrees of Freedom (df)
Mean Square
(MS)
Factor
(Between)
27.82
Error
(Within)
Total
543.05
159
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 8 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)
27.82
Error
(Within)
Total
543.05
159
N/A
Explanation / Answer
Solution(a) : ANOVA Table-
(b) Test Statistic is calculated mean square factor / mean square error = .05399
(c) P-value will be P[ F( 7, 152) > .05399 ] = .00023
(d) As p-value is less than .05 then we can say that null hypothesis is rejected at 5% level of significance and we can conclude that mean weight loss is not same for the 8 programs.
Answer
TY!
Source of variation sum of squares degree of freedom mean square Factor( between ) 27.82 8-1 = 7 27.82/7 = 3.9743 Error (within) 543.05 -27.82 = 515.23 160-8 = 152 515.23/152 = 3.3897 TOtal 543.05 159 = 3.9743 + 3.3897 = 7.364Related Questions
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