In a completely randomized experimental design, 7 experimental units were used f
ID: 3223968 • Letter: I
Question
In a completely randomized experimental design, 7 experimental units were used for the first treatment, 9 experimental units for the second treatment, and 14 experimental units for the third treatment. Part of the ANOVA table for this experiment is shown below.
Source of Variation
Sum of
Squares
Degrees of
Freedom
Mean
Square
F
Between Treatments
_____?
_____?
_____?
4.5
Within Treatments (Error)
_____?
_____?
4
Total
_____?
_____?
a.
Fill in all the blanks in the above ANOVA table.
b.
At a 5% level of significance, test to see if there is a significant difference among the means.
STEP BY STEP SOLUTIONS PLEASE!
Source of Variation
Sum of
Squares
Degrees of
Freedom
Mean
Square
F
Between Treatments
_____?
_____?
_____?
4.5
Within Treatments (Error)
_____?
_____?
4
Total
_____?
_____?
Explanation / Answer
We have three tretments and number of observations are 30 (7+9+14)
a)
b) H0: There is no difference between means of thtree treatments
H1: There is a difference between means of thtree treatments
alpha:5%
Test statistic:
F cal=4.5
Conclusion:
F critical value at (2,27) degrees of freedom is 3.345
F cal > F critical value, we reject the H0. Hence claim is signifcant.
Source of Variation Sum of Degrees of Mean Squares Freedom Square F Between Treatments 18*2=36 3-1=2 4.5*4=18 4.5 Within Treatments (Error) 27*4=108 29-2=27 4 Total 108+36 =144 30-1=29