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).

Question

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:

$$M{S}_{T}reatment=\frac{S{S}_{T}reatment}{d{f}_{T}reatment}$$

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.