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Answer:
Step-by-step explanation:
Hello!
You have the information of an analysis of variance of 1 factor with 3 treatments.
Treatment 1 has 11 experimental units.
Treatment 2 has 14 experimental units.
Treatment 3 has 20 experimental units.
The whole experiment has a total sze of n= 11+14+20= 45 experimental units.
Unfortunatelly only with the sample size you cannot calculate all values of the ANOVA table, you need at least the information of either two Sum of Squares (SS) or one Sum of Squares and one Means Square (MS).
Tha first attachments shows how to construct the table by hand.
I'll use as example the following data:
SSTr= 1200
SSTotal= 1800
The Total SS is obtained by adding the SS of Treatmets + SS of error, so the SSerror is:
SSerror= SSTotal - SSTr= 1800 - 1200= 600
To calculate each Mean Square you have to divide the SS by the Degrees of Freedom, so next step is to calculate the Degrees of Freedom:
DFTr= k-1
Where k represents the number of Treatmets of the experiment.
DFTr= 3-1= 2
DFerror= n-k
DFerror= 45-3= 42
DFTotal= n-1= 45-1= 44
Now you can calculate the MS
MSTr= SSTr/DFTr= 1200/2= 600
MSerror= SSerror/DFerror= 600/42= 14,2857≅ 14.29
And the next step is to calculate the value of the test:
F= MSTr/MSerror= 600/14.29= 41,99
Finally the p-value.
The hypothesis test of ANOVA is one-tailed to the right under the Stedecors-F distribution with degrees of fredom (DFTr;DFerror)
The P-value is
P(≥41.99)= 1 - P(
<41.99)= 1 - 0.9999= 0,0001
I hope it helps!
