Question

In: Statistics and Probability

Fifteen people are randomly assigned, so that 5 people exercise in the morning, afternoon, or night....

Fifteen people are randomly assigned, so that 5 people exercise in the morning, afternoon, or night. After 8 weeks, their weight loss is measured in pounds. Compute the F ratio.

Morning Afternoon     Night      
10 8 6
8 8 7
7 9 5
5 7 4
9 7 5

Solutions

Expert Solution

Applying one way ANOVA:

Morning Afternoon Night
10 8 6
8 8 7
7 9 5
5 7 4
9 7 5
count ni= 5 5 5
Average==ΣXi/ni= 7.8000 7.8000 5.4000
Total=ΣX2i   =   319.000 307.0000 151.0000
SS=ΣX2i -(Σxi)2/ni= 14.800 2.8000 5.2000
Grand average Xgrand =∑xi/N = 105/10= 7.0000
i ni i ni*(Xi-Xgrand)2 SS=(ni-1)*s2
Morning 5 7.8000 3.200 14.8
Afternoon 5 7.8000 3.200 2.8
Night 5 5.4000 12.800 5.2
Total 15 19.200 22.8000
SSTr SSE
df treatments = number of treatments-1= 2
df error = N-k= 15-3= 12
df total= N-1= 15-1= 14
MS(treatment) =SSTr/df(Tr)=19.2/2= 9.60000
MS(error) =SSE/df(error)=22.8/12= 1.90000
test statistic F ratio =MSTr/MSE =9.6/1.9= 5.0526

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