Improve Your Understanding of College Level Statistics Problems

The following table summarizes the results of a study on SAT prep courses, comparing SAT scores of students in a private preparation class, a high school preparation class, and no preparation class. Use the information from the table to answer the remaining questions. 
$\begin{array}{|cccc|}\hline \text{Treatment}& \text{Number of Observations}& \text{Sample Mean}& \text{Sum of Squares (SS)}\\ \text{Private prep class}& 60& 680& 265,500.00\\ \text{High school prep class}& 60& 650& 276,120.00\\ \text{No prep class}& 60& 635& 302,670.00\\ \hline\end{array}$ 
Using the data provided, complete the partial ANOVA summary table that follows (Hint: T, the treatment total, can be calculated as the sample mean times the number of observations G, the grand total, can be calculated from the values of T once you have calculated them.) 
$\begin{array}{|cccc|}\hline \text{Source}& \text{Sum of Squares (SS)}& df& \text{Mean Square (MS)}\\ \text{Between treatments}& & & \\ \text{Within treatments}& & & \\ \hline\end{array}$ 
ANOVA summary tables typically have a "Total" row not induded in the partial table you just completed. Which of the following is a possible reason for induding this row? 
a) The ${\displaystyle M{S}_{\to tal}}$ is used in the calculation of the F test statistic. 
b) The ${\displaystyle S{S}_{\to tal}}$ is used in the calculation of the F test statistic. 
c) The total sums of squares is the sometimes called the "error term" 
d) The $S{S}_{total}$ is sometimes easier to calculate than. $S{S}_{between}$ Since $S{S}_{within}+S{S}_{between}=S{S}_{total}$, you can use $S{S}_{total}$ to calculate $S{S}_{between}$.
In ANOVA, the F test statistic is the ? of the between-treatments variance and the within-treatments variance. the value of the F test statistic is ? 
When the null hypothesis is true, the F test statistic is ? When the null hypotesis is false, the F test statistic is most likely ? In general, you should reject the null hypotesis for.