Consider the following table for a single-factor ANOVA.

Level of Factor
Replicates 1 2 3
1 0 4 4
2 0 5 6
3 1 3 6

(a) Find x1,2.


(b) Find x2,1.


(c) Find C1.


(d) Find x.


(e) Find (Ci )2.

In order to answer these questions about a single-factor ANOVA table, we need to understand the components of the table and the formulas involved.

The components of a single-factor ANOVA table are as follows:

- The levels of the factor: These are the different categories or treatments being compared.
- The replicates: These are the different trials or observations within each level of the factor.
- The values: These are the actual data points or measurements for each combination of level and replicate.

Now let's go through each question step by step:

(a) Find x1,2:
- To find x1,2, we need to locate the value for level 1 and replicate 2, which is 5 in this case.

(b) Find x2,1:
- To find x2,1, we need to locate the value for level 2 and replicate 1, which is 0 in this case.

(c) Find C1:
- To find C1, we need to sum up the values for all replicates under level 1.
- For level 1, the values are 0, 4, and 4.
- Adding these values together, we get C1 = 0 + 4 + 4 = 8.

(d) Find x:
- To find x, we need to sum up all the values in the table.
- Adding up all the values in the table, we get x = 0 + 4 + 4 + 0 + 5 + 6 + 1 + 3 + 6 = 29.

(e) Find (Ci )^2:
- To find (Ci )^2, we need to square the sum of values for each level.
- For level 1, the sum of values is 8 (from part c). Squaring this, we get (C1)^2 = 8^2 = 64.
- Similarly, for level 2, the sum of values is 11, so (C2)^2 = 11^2 = 121.
- For level 3, the sum of values is 10, so (C3)^2 = 10^2 = 100.

So, the answers to the questions are:
(a) x1,2 = 5
(b) x2,1 = 0
(c) C1 = 8
(d) x = 29
(e) (C1)^2 = 64, (C2)^2 = 121, (C3)^2 = 100.