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Hypothesis Testing

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A dietician wanted to test 3 different diets to find out if the mean weight loss for each of these is the same. She randomly selected 21 overweight persons, randomly divided them into 3 groups, put each group into one of three diets. The following table records the weights (in pounds) lost by each persons after being on these diets for 2 months.

Diet I Diet II Diet III
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 3 diets is the same. Write the null & alternative hypotheses.
b) Show the rejection & non rejection regions of the F distribution for α = .025
c) Calculate SSB, SSW, and SST
d) What are the degrees of freedom for the numerator and denominator?
e) Calculate the Mean Squares for between and within
f) What is the critical value of F for alpha= .025 (i.e. the table value).
g) What is the calculated value of the test statistic F?
h) Do you accept or reject the null hypothesis?

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Solution describes the step by step method to test if the mean weight lost by all persons on each of the 3 diets is the same.

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Please refer attached file for complete solution. Expressions typed with the help of equation writer and images used are missing here.

a) We are to test if the mean weight lost by all persons on each of the 3 diets is the same. Write the null & alternative hypotheses.
(Mean weight loss by all persons on each of the 3 diets is the same)
H1: All are not equal

b) Show the rejection & non rejection regions of the F distribution for α = .025

c) Calculate SSB, SSW, and SST

Diet 1 Diet 2 Diet 3
15 11 9
8 16 17
...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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