A study of 8 different weight loss programs involved 240 subjects. Each of the 8
ID: 3269358 • Letter: A
Question
A study of 8 different weight loss programs involved 240 subjects. Each of the 8 programs had
30 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):
(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.
Explanation / Answer
a)
Factor(between) df = k-1 = 7(Since there are 8 different weight loss programmes , k =8)
Error df = n-k = 240 - 8 = 232
SS(Error) = SS(Total) - SS (Between)
= 553.05 - 42.5
= 510.55
MS(Factor) = SS (Fator) / DF (Factor)
= 42.5 / 7
= 6.07143
MS(Within) = SS(Within) / DF (Within)
= 510.55 / 232
= 2.20065
F Value = MS(Between) / MS(Within)
= 6.07143 / 2.20065
= 2.7589
ANOVA Table
Source DF SS MSS F
Between 7 42.5 6.07143 2.75893
Error 232 510.55 2.20065
Total 239 553.05
b)
Test statistics F = MS(Between) / MS(Within)
= 6.07143/2.20065
= 2.7589
c)
p value from test statistics is 0.009013.
d)
Since p value < 0.05 level, we have sufficient evidence to reject H0.
We conclude that at 0.05 level, we have sufficient evidence to support the claim that the mean weight loss is the
same for the 8 programmes.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.