Consider the partial ANOVA table shown below. Let a = .01
Source of Variation 
DF 
SS 
MS 
F 
Between Treatments 
3 
180 

Within Treatments (Error) 

Total 
19 
380 
If all the samples have five observations each:
there are 10 possible pairs of sample means. 

the only appropriate comparison test is the TukeyKramer. 

all of the absolute differences will likely exceed their corresponding critical values. 

there is no need for a comparison test – the null hypothesis is not rejected. 
2 points
QUESTION 2
Consider the partial ANOVA table shown below. Let a = .01
Source of Variation 
DF 
SS 
MS 
F 
Between Treatments 
3 
180 

Within Treatments (Error) 

Total 
19 
380 
The mean square within treatments (MSE) is
12.5 

200 

16 

60 
2 points
QUESTION 3
Consider the partial ANOVA table shown below:
Source of Variation 
DF 
SS 
MS 
F 
Between Treatments 
64 
8 

Within Treatments (Error) 
2 

Total 
100 
The number of degrees of freedom corresponding to within treatments is
20 

18 

4 

5 
2 points
QUESTION 4
Consider the following ANOVA table.
Source of Variation 
SS 
df 
MS 
F 
Treatment 
49411.11 
2 
24705.56 
10.4304 
Error 
35529.17 
15 
2368.611 

Total 
84940.28 
17 
The appropriate null hypothesis is:
mu1 = mu2 

mu1 = mu2 = mu3 

At least one mean is different. 

The populations are independent. 
2 points
QUESTION 5
The following information is from a 1way ANOVA involving three treatments:
Treatment 1 
Treatment 2 
Treatment 3 

Sample Size 
5 
10 
5 
Sample Mean 
4 
8 
9 
The overall mean for all the treatments is
7.25 

4.89 

6.67 

7.00 
source  df  SS  MS  F  Fcrit 
between  3  180  60  4.8  5.29 
within  16  200  12.5  
total  19  380 
1)
there is no need for a comparison test – the null hypothesis is not rejected.
2)
mean square within treatments (MSE) is =12.5
3)
source  df  SS  MS  F  Fcrit 
between  4  64  16  8  4.58 
within  18  36  2  
total  22  100 
number of degrees of freedom corresponding to within treatments is =18
4)
mu1 = mu2 = mu3
5)
overall mean for all the treatments is =(4*5+8*10+9*5)/(5+10+5)=7.25
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