You are given an ANOVA table below with some missing entries. Source Variation S
ID: 3223588 • Letter: Y
Question
You are given an ANOVA table below with some missing entries.
Source
Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F
Between Treatments
3
1,198.8
Between Blocks
5,040
6
840
Error
5,994
18
Total
27
1. Calculate the Sums of Squares Total (SST)?
2. Calculate the correct F statistic for the treatment?
3. At the 0.01 level of significance, what is your statistical decision?
4. Calculate the Sums of Squares Treatment (SSTR)?
5. At the 0.01 level of significance, what is your busines related recommendation?
There is not enough evidence to show any difference among the treatment groups; all group means are the same.
There is suffcient evidence that all the group means differ from each other.
There is sufficient evidence that at least one group mean differs from the rest.
Cannot make a business related recommendation based on this sample data.
Source
Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F
Between Treatments
3
1,198.8
Between Blocks
5,040
6
840
Error
5,994
18
Total
27
Explanation / Answer
4) Treatment sum of squares = Mean square for treatments *DF= 1198.8*3 = 3596.4
1) Total Sum of squares= 3596.4+5040+5994 = 14630.4
Error mean squre= 5994/18 = 333
3) F statistic for tratments = Mean square for treatments/Error mean squre = 1198.8/333 = 3.6
F statistic for blocks= 840/333 = 2.5225
at 0.01 level of significance F critical value for treatments at (3,18)= 5.0919
at 0.01 level of significance F critical value for blocks at (6,18)= 4.0146
3) Statistical Decision: There is not enough evidence to show any difference among the treatment groups; all group means are the same.
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