We are given an ANOVA table with some missing values. We are given that the number of groups $k = 4$. We have the following information: - $SS_{Between} = 97.40$ - $SS_{Total} = 189.25$ - $df_{Total} = 33$ We need to complete the ANOVA table by finding the missing values: - $df_{Between}$ - $SS_{Within}$ - $df_{Within}$ - $MS_{Between}$ - $MS_{Within}$ - $F$

1. Problem Description

We are given an ANOVA table with some missing values. We are given that the number of groups $k = 4$. We have the following information:

- $SS_{Between} = 97.40$

- $SS_{Total} = 189.25$

- $df_{Total} = 33$

We need to complete the ANOVA table by finding the missing values:

- $df_{Between}$

- $SS_{Within}$

- $df_{Within}$

- $MS_{Between}$

- $MS_{Within}$

- $F$

2. Solution Steps

First, let's find $df_{Between}$. Since $k = 4$, we have:

$df_{Between} = k - 1 = 4 - 1 = 3$

Next, let's find $SS_{Within}$. We know that $SS_{Total} = SS_{Between} + SS_{Within}$, so:

$SS_{Within} = SS_{Total} - SS_{Between} = 189.25 - 97.40 = 91.85$

Now, let's find $df_{Within}$. We know that $df_{Total} = df_{Between} + df_{Within}$, so:

$df_{Within} = df_{Total} - df_{Between} = 33 - 3 = 30$

Next, let's find $MS_{Between}$. We have $MS_{Between} = \frac{SS_{Between}}{df_{Between}}$, so:

$MS_{Between} = \frac{97.40}{3} \approx 32.4667$

Now, let's find $MS_{Within}$. We have $MS_{Within} = \frac{SS_{Within}}{df_{Within}}$, so:

$MS_{Within} = \frac{91.85}{30} \approx 3.0617$

Finally, let's find $F$. We have $F = \frac{MS_{Between}}{MS_{Within}}$, so:

$F = \frac{32.4667}{3.0617} \approx 10.604$

3. Final Answer

$df_{Between} = 3$

$SS_{Within} = 91.85$

$df_{Within} = 30$

$MS_{Between} = 32.47$ (rounded to two decimal places)

$MS_{Within} = 3.06$ (rounded to two decimal places)

$F = 10.60$ (rounded to two decimal places)