20 A study of 15 different weight loss programs involved 300 subjects. Each of t
ID: 3356390 • Letter: 2
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20 A study of 15 different weight loss programs involved 300 subjects. Each of the 15 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 15 programs (a) Complete the following ANOVA table with sum of squares, degrees of freedom, and mean square (Show all work) Mean Square (MS) Sum of Squares Degrees of Freedom Source of Variation Factor (Between) EiTor (Within) Total 53.6 N/A 553.05 299 (b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit. Is there sufficient evidence to support the claim that the mean weight loss is the same for the 15 programs at the significance level of 0.01? Explain. (c) (d)Explanation / Answer
a) from above table:
b) from above test statistic F=MS(factor)/MS(error) =3.829/1.752=2.185
c) for above test statistic and 14 and 285 degree of freedom in numerator and denominator ; p value =0.0085
d) as p value is less then 0.01 level ; tehrefore we reject null hypothesis,
we have sufficient evidence to conclude that mean weight loss is different for at least 2 programmes
source of variation SS df MS factor(between) 53.6 15-1=14 53.6/14=3.829 error(within) 553.05-53.6=499.45 299-14=285 499.45/285=1.752 total 553.05 299Related Questions
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