Question

Consider the following partially completed ANOVA, and answer the following: give the value of (A). / Beskou die onvoltooide ANOVA en beantwoord die volgende: gee die waarde van (A).
ANOVA

Source SS df MS Fstat Ftab
Treatment (A) 2 43 024.778 25.1754 (F)
Error 10 254 (C) (E)
Total (B) (D)

Answer 1

To find the value of (A) in the given ANOVA table, we can use the relationship among the sum of squares (SS), degrees of freedom (df), mean squares (MS), and F-statistic.

Given the ANOVA structure, we know that:
- Total Sum of Squares (SS_Total) = SS_Treatment + SS_Error
- Total Degrees of Freedom = df_Treatment + df_Error + df_Total

Let's break down the provided information:

1. SS_Treatment = (A)
2. df_Treatment = 2
3. MS_Treatment = 43,024.778 (which is calculated as SS_Treatment / df_Treatment)
4. F_stat = 25.1754 (which is calculated as MS_Treatment / MS_Error)

Since you have both the MS_Treatment and the df_Treatment, we can find SS_Treatment (A) as follows:

\[
MS_Treatment = \frac{SS_Treatment}{df_Treatment}
\]

Plugging in the numbers:

\[
43,024.778 = \frac{A}{2}
\]

Now, we can cross-multiply to solve for \(A\):

\[
A = 43,024.778 \times 2 = 86,049.556
\]

Thus, the value of (A) is approximately **86,049.556**.