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Complete the ANOVA table. Round to two decimals if needed. Note that "Factor" = "Between" and "Error" = "Within."

[tex]\[
\begin{tabular}{|r|c|r|r|r|}
\hline
\text{Source} & \text{SS} & \text{d.f.} & \text{MS} & \text{F} \\
\hline
\text{Factor} & 55 & 5 & \square & \square \\
\hline
\text{Error} & 39 & 14 & \square & \\
\hline
\end{tabular}
\][/tex]

a. [tex]$MS_B=$[/tex] [tex]$\square$[/tex]

b. [tex]$MS_W=$[/tex] [tex]$\square$[/tex]

c. [tex]$F=$[/tex] [tex]$\square$[/tex]

Sagot :

GinnyAnsweridn
Let's complete the ANOVA table step-by-step:

1. Sum of Squares for Factor (SS_B): Given as 55.

2. Degrees of Freedom for Factor (df_B): Given as 5.

3. Sum of Squares for Error (SS_W): Given as 39.

4. Degrees of Freedom for Error (df_W): Given as 14.

Next, we need to calculate the Mean Square for the Factor (MS_B) and Mean Square for the Error (MS_W), and then the F-value.

Mean Square for Factor (MS_B):
[tex]\[ MS_B = \frac{SS_B}{df_B} = \frac{55}{5} = 11.0 \][/tex]

Mean Square for Error (MS_W):
[tex]\[ MS_W = \frac{SS_W}{df_W} = \frac{39}{14} \approx 2.79 \][/tex]

F-value:
[tex]\[ F = \frac{MS_B}{MS_W} = \frac{11.0}{2.79} \approx 3.95 \][/tex]

So, to complete the ANOVA table:

a. [tex]\( MS_B = 11.00 \)[/tex]

b. [tex]\( MS_W = 2.79 \)[/tex]

c. [tex]\( F = 3.95 \)[/tex]

Here's the completed ANOVA table:

[tex]\[ \begin{array}{|r|c|r|r|r|} \hline \text{Source} & \text{SS} & \text{d.f.} & \text{MS} & \text{F} \\ \hline \text{Factor} & 55 & 5 & 11.00 & 3.95 \\ \hline \text{Error} & 39 & 14 & 2.79 & \\ \hline \end{array} \][/tex]
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