Question

You may need to use the appropriate technology to answer this question. In a completely randomized design, 11 experimental units were used for the first treatment, 14 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.)

Answer 1

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)

$F_{DFTr;DFerror}= F_{2;42}$

The P-value is

P($F_{2;42}$≥41.99)= 1 - P($F_{2;42}$<41.99)= 1 - 0.9999= 0,0001‬

I hope it helps!