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)
Answers
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Answered by
GPT-4o mini
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**.
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**.
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