24) An example was conducted that called for an ANOVA test. Sample of 16 observa
ID: 3180492 • Letter: 2
Question
24) An example was conducted that called for an ANOVA test. Sample of 16 observations were obtained from each of 5 populations (80 observations in all). Some of the relevant date are shown in the following ANOVA table:
Source of variation
Sum of squares
Degrees of freedom
Mean square
F
Between group
97.3
Within group
Total
1845.6
The computed F-ratio will equal:
A-0.73
B-2.50
C-5.01
D-5.30
Source of variation
Sum of squares
Degrees of freedom
Mean square
F
Between group
97.3
Within group
Total
1845.6
Explanation / Answer
Given
Number of Groups =5
Total number of observations = 80
Degrees of freedom for between groups = Number of groups - 1 = 5-1 = 4
Degrees of freedom for total = Number of observations - 1 = 80 - 1 =79
Degrees of freedom for Within Group = Degrees of freedom for total - Degrees of freedom for between groups
= 79-4 = 75
Mean sum of squares - Between Group = Sum of Squares between group / Degrees of freedom for between groups
Therefore ,
Sum of Squares between group = Mean sum of squares for Between Group x Degrees of freedom for between groups
Given ,
Mean sum of squares for Between Group = 97.3
Sum of Squares between group = 97.3 x 4 = 389.2
Sum of squares of within group = Total sum of squares - Sum of squares of between group
Given ,
Total sum of squares = 1845.6
Sum of squares of within group = Total sum of squares - Sum of squares of between group
= 1845.6 - 389.2 = 1456.4
Mean Sum of squares within group = Sum of squares within group / Degrees of freedom within Group
=1456.4/75 = 19.4187
F-ration = Mean Sum of Sqaures between Group / Mean Sum of Sqaures within Group
= 97.3 / 19.4187 = 5.0101
Answer . C. 5.01
Source of variation Sum of squares Degrees of freedom Mean square F Between group 389.2 4 97.3000 5.01 Within group 1456.4 75 19.4187 Total 1845.6 79Related Questions
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