Question

Consider the following partially completed ANOVA and give the value of (c). / Beskou die onvoltooide ANOVA en gee die waarde van (c).


Source SS df MS Fstat Ftab
Treatments 142.67 (d) 35.6675 (g) (i)
Blocks 68.14 5 (f) (h) (j)
Errors (b) 20 1.9165
Total (c) (e)

Answer 1

To complete the ANOVA table and find the value for (c), we need to use the following relationships:

1. Total Sum of Squares (SS_total) is the sum of the Treatment SS, Block SS, and Error SS:
\[
SS_{total} = SS_{treatments} + SS_{blocks} + SS_{errors}
\]

2. The degrees of freedom (df) for each component can be found using:
- df for treatments = k - 1 (where k is the number of treatment groups)
- df for blocks = b - 1 (where b is the number of blocks)
- df for errors = (k - 1)(b - 1)
- Total df = df for treatments + df for blocks + df for errors

Given:
- SS_treatments = 142.67
- SS_blocks = 68.14
- SS_errors = b (unknown, but we have df = 20)

Let's denote:
- SS_errors = b
- Total SS = c
- Total df = e
- df_treatments = d
- df_blocks = 5
- df_errors = 20

To find \( c \):
\[
c = 142.67 + 68.14 + b
\]

Next, we note that the total df:
\[
e = d + 5 + 20
\]

Also, since we know \( MS = \frac{SS}{df} \):

1. For Blocks, we can calculate \( MS_{blocks} \):
\[
MS_{blocks} = \frac{68.14}{5} = 13.628
\]
So, \( f = 13.628 \).

2. For Errors, since \( MS_{errors} = 1.9165 \) (given), but we don't have \( SS_{errors} \) yet.

### Finding \( SS_{errors} \) using \( MS \):
We have:
\[
MS_{errors} = \frac{SS_{errors}}{df_{errors}}
\]
This gives us:
\[
SS_{errors} = MS_{errors} \times df_{errors} = 1.9165 \times 20 = 38.33
\]
Now, substitute back:
\[
SS_{total} = SS_{treatments} + SS_{blocks} + SS_{errors} = 142.67 + 68.14 + 38.33
\]
Calculating:
\[
SS_{total} = 249.14
\]
So, the value of \( c \) is:
\[
c = 249.14
\]

### Thus, the final answer is:
**(c) = 249.14**