The problem provides an ANOVA table with some missing values. We need to calculate the missing values in the table, specifically the Sum of Squares (SS) for 'Between' and 'Within', and the Mean Square (MS) for 'Between'. We also need to calculate the total degrees of freedom and total Sum of Squares. Finally, we need to find the F statistic.

1. Problem Description

The problem provides an ANOVA table with some missing values. We need to calculate the missing values in the table, specifically the Sum of Squares (SS) for 'Between' and 'Within', and the Mean Square (MS) for 'Between'. We also need to calculate the total degrees of freedom and total Sum of Squares. Finally, we need to find the F statistic.

2. Solution Steps

The ANOVA table provides information to calculate the F statistic, which tests for differences between group means. The table is structured as follows:

Source | df | SS | MS | F

------- | -------- | -------- | -------- | --------

Between | $df_B$ | $SS_B$ | $MS_B$ | F

Within | $df_W$ | $SS_W$ | $MS_W$ |

Total | $df_T$ | $SS_T$ | |

We are given the following information:

* $df_B = 2$ (degrees of freedom between)

* $MS_B = 44.96$ (mean square between)

* $df_W = 54$ (degrees of freedom within)

* $MS_W = 2.48$ (mean square within)

We can calculate the Sum of Squares using the formula:

$SS = df \times MS$

* $SS_B = df_B \times MS_B = 2 \times 44.96 = 89.92$

* $SS_W = df_W \times MS_W = 54 \times 2.48 = 133.92$

The total degrees of freedom is the sum of the degrees of freedom between and within:

$df_T = df_B + df_W = 2 + 54 = 56$

The total sum of squares is the sum of the sum of squares between and within:

$SS_T = SS_B + SS_W = 89.92 + 133.92 = 223.84$

The F statistic is calculated as:

$F = \frac{MS_B}{MS_W} = \frac{44.96}{2.48} = 18.12903226 \approx 18.13$

3. Final Answer

SS Between = 89.92

SS Within = 133.92

df Total = 56

SS Total = 223.84

F = 18.13