A pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, three samples of rats are selected with $n=10$ in each sample. The first sample receives the drug every day. The second sample is given the drug once a week, and the third sample receives no drug at all (the control group). The dependent variables is the amount of food eaten by each rat over a 1-month period. These data are analyzed by an ANOVA, and the results are reported in the following summary table. Fill in all missing values in the table. (Hint: Start with the $d f$ column.) \begin{tabular}{|c|c|c|c|c|} \hline & S.S. & d.f. & M.S. & $F$ \\ \hline Between & & & & \\ \hline & & & \\ \hline & & & & \\ \hline \end{tabular} What is the Critical Value for this data? Use the $5 \%$ significance level. Table of Critical Values ${ }^{\text {ק }}$ critical value $=$ Report answer accurate to at least 2 decimal places.

Step 1 ：To fill in the missing values in the table, we need to understand the structure of an ANOVA table. The degrees of freedom (df) for the "Between" group is calculated as the number of groups minus 1. In this case, we have 3 groups (daily drug, weekly drug, and control), so df for the "Between" group is 3 - 1 = 2. The total degrees of freedom is the total number of observations minus 1. We have 3 groups of 10 rats each, so the total df is 30 - 1 = 29. The degrees of freedom for the "Within" group (also known as "Error" or "Residual") is the total df minus the "Between" df. So, df for the "Within" group is 29 - 2 = 27. The Mean Square (MS) is the Sum of Squares (SS) divided by the df for each group. So, MS for the "Between" group is SS_Between / df_Between, and MS for the "Within" group is SS_Within / df_Within. The F statistic is the ratio of the "Between" MS to the "Within" MS, or F = MS_Between / MS_Within. The table should now look like this: \begin{tabular}{|c|c|c|c|c|} \hline & S.S. & d.f. & M.S. & $F$ \\ \hline Between & SS_Between & 2 & MS_Between & F \\ \hline Within (Error) & SS_Within & 27 & MS_Within & \\ \hline Total & SS_Total & 29 & & \\ \hline \end{tabular} The critical value for this data at the 5% significance level can be found in an F-distribution table or calculated using statistical software. The critical value is the value of F that the observed F statistic must exceed for the null hypothesis to be rejected. It depends on the degrees of freedom for the "Between" and "Within" groups. In this case, with df1 = 2 and df2 = 27, the critical value at the 5% significance level is approximately 3.35 (this value may vary slightly depending on the source of the F-distribution table).