A dietition wanted to test three different diets to these diets is the same. She randomly selected 21 into three groups, and put each group on one of t the weights (In kg) loss by these persons after bein Diet 1 Diet 2

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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on ANOVA
1. A dietition wanted to test three different diets to find out if the mean weight loss for each of
these diets is the same. She randomly selected 21 overweight person, randomly divided them
into three groups, and put each group on one of the three diets. The following table records
the weights (In kg) loss by these persons after being on these diets for two months.
Diet 1
Diet 2
Diet 3
15
11
9
8
16
17
17
9
11
7
16
8
26
24
15
12
20
6
8
19
14
a) We are to test if the mean weight lost by all persons on each of the three diets is the same.
Write the null and alternative hypotheses.
b) Show the rejection and nonrejection regions on the F distribution curve for a=0.025.
c) Calculate SSB, SSW, and SST.
d) What are the degrees of freedom for the numerator and denominator?
e) Calculate the between-samples and within-samples variances.
f) What is the critical value of F for α=0.025.
g) What is the calculated value of the test statistic F?
h) Write the ANOVA table for this exercise.
i) Will you reject the null hypotheses stated in part a at a sigfnificance level of 2.5%?
Transcribed Image Text:Exercise on ANOVA 1. A dietition wanted to test three different diets to find out if the mean weight loss for each of these diets is the same. She randomly selected 21 overweight person, randomly divided them into three groups, and put each group on one of the three diets. The following table records the weights (In kg) loss by these persons after being on these diets for two months. Diet 1 Diet 2 Diet 3 15 11 9 8 16 17 17 9 11 7 16 8 26 24 15 12 20 6 8 19 14 a) We are to test if the mean weight lost by all persons on each of the three diets is the same. Write the null and alternative hypotheses. b) Show the rejection and nonrejection regions on the F distribution curve for a=0.025. c) Calculate SSB, SSW, and SST. d) What are the degrees of freedom for the numerator and denominator? e) Calculate the between-samples and within-samples variances. f) What is the critical value of F for α=0.025. g) What is the calculated value of the test statistic F? h) Write the ANOVA table for this exercise. i) Will you reject the null hypotheses stated in part a at a sigfnificance level of 2.5%?
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