The problem is to complete the ANOVA table. We are given $N=16$, $df_{Between} = 2$, $MS_{Between} = 14.10$, and $SS_{Total} = 64.65$. We need to calculate $SS_{Between}$, $SS_{Within}$, $df_{Within}$, $df_{Total}$, $MS_{Within}$, and $F$.

1. Problem Description

The problem is to complete the ANOVA table. We are given $N=16$, $df_{Between} = 2$, $MS_{Between} = 14.10$, and $SS_{Total} = 64.65$. We need to calculate $SS_{Between}$, $SS_{Within}$, $df_{Within}$, $df_{Total}$, $MS_{Within}$, and $F$.

2. Solution Steps

Step 1: Calculate $SS_{Between}$.

$SS_{Between} = df_{Between} \times MS_{Between} = 2 \times 14.10 = 28.20$

Step 2: Calculate $SS_{Within}$.

$SS_{Total} = SS_{Between} + SS_{Within}$

$SS_{Within} = SS_{Total} - SS_{Between} = 64.65 - 28.20 = 36.45$

Step 3: Calculate $df_{Total}$.

$df_{Total} = N - 1 = 16 - 1 = 15$

Step 4: Calculate $df_{Within}$.

$df_{Total} = df_{Between} + df_{Within}$

$df_{Within} = df_{Total} - df_{Between} = 15 - 2 = 13$

Step 5: Calculate $MS_{Within}$.

$MS_{Within} = \frac{SS_{Within}}{df_{Within}} = \frac{36.45}{13} = 2.8038 \approx 2.80$

Step 6: Calculate F.

$F = \frac{MS_{Between}}{MS_{Within}} = \frac{14.10}{2.8038} = 5.028 \approx 5.03$

3. Final Answer

$SS_{Between} = 28.20$

$SS_{Within} = 36.45$

$df_{Within} = 13$

$df_{Total} = 15$

$MS_{Within} = 2.80$

$F = 5.03$