Sure, let's perform a step-by-step calculation to determine the total sum of squares ([tex]\(SS_{\text{total}}\)[/tex]) for the given ANOVA problem.
1. Determine the total number of observations (N):
Given that there are 3 groups and each group has [tex]\(n = 5\)[/tex] observations:
[tex]\[
k = 3 \quad(\text{number of groups})
\][/tex]
[tex]\[
N = n \times k = 5 \times 3 = 15 \quad(\text{total number of observations})
\][/tex]
2. Calculate the grand total (G):
Sum the totals from all groups:
[tex]\[
G = T_1 + T_2 + T_3 = 10 + 15 + 5 = 30
\][/tex]
3. Calculate [tex]\(G\)[/tex] squared divided by the total number of observations:
[tex]\[
\frac{G^2}{N} = \frac{30^2}{15} = \frac{900}{15} = 60
\][/tex]
4. Calculate the sum of squares total ([tex]\(SS_{\text{total}}\)[/tex]):
Given [tex]\(\sum X^2 = 94\)[/tex]:
[tex]\[
SS_{\text{total}} = \sum X^2 - \frac{G^2}{N} = 94 - 60 = 34
\][/tex]
Therefore, the total sum of squares ([tex]\(SS_{\text{total}}\)[/tex]) is:
[tex]\[
SS_{\text{total}} = 34
\][/tex]
So, the correct answer is:
[tex]\[
34
\][/tex]
