Part B
the three levels of the factor. (2 points each; 6 points total)
Source of Variation |
Sum of Squares |
Degrees of Freedom |
Mean Square |
F |
Treatment |
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Error |
432076.5 |
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Total |
675643.3 |
means for the three levels of the factors are the same.
a) Number of treatment, k = 3
Total sample Size, N = 6*3 = 18
df(between) = k-1 = 2
df(within) = N-k = 15
df(total) = N-1 = 17
SS(within) = 432076.5
SS(total) = 675643.3
SS(between) = SS(total) - SS(within) = 675643.3 - 432076.5 = 243566.8
MS(between) = SS(between)/df(between) =121783.4
MS(within) = SS(within)/df(within) =28805.1
F = MS(between)/MS(within) = 4.2278
Source of variation | SS | df | MS | F |
Treatment | 243566.8 | 2 | 121783.4 | 4.2278 |
Error | 432076.5 | 15 | 28805.1 | |
Total | 675643.3 | 17 |
b) At α = 0.05, df1=2, df2 =15 Critical value, Fc = F.INV.RT(0.05, 2, 15) = 3.682
c) As F = 4.2278 > Fc = 3.682, we reject the null hypothesis.
There is not enough evidence to conclude that the population means for the three levels of the factors are the same at 0.05 significance level.
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