In: Statistics and Probability
Source of Variation |
Sum of Squares |
Degrees of Freedom |
Mean Square |
F |
Treatment |
||||
Error |
432076.5 |
|||
Total |
675643.3 |
ANSWER::
Here ,
Number of treatments k = 3
Each treatments contains 2 points
So , N = 3 * 2 = 6
degrees of freedom for treatments = k - 1 = 3 - 1 = 2
degrees of freedom for errors = n - k = 6 - 3 = 3
degrees of freedom for Total = N - 1 = 6 - 1 = 5
Treatment sum of squares = Total sum of squares - Error sum of squares
= 675643.3 - 432076.5
= 243566.8
Now ,
Mean square = Sum of squares/Degrees of freedom
F = Mean square(treatment) / Mean square(error)
a)
Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F ratio |
Treatment | 243566.8 | 2 | 121783.4 | 0.8456 |
Error | 432076.5 | 3 | 144025.5 | |
Total | 675643.3 | 5 |
b)
= 0.05
Critical value of the test
= F0.05 , df1 , df2
= F0.05,2,3
= 9.552
(Use f distribution table)
c)
Since F = 0.8456 < F0.05,2,3 , we do not reject the null hypothesis.
We conclude that
the population means for the three levels of the factors are not significantly different.
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