1. **State the problem:** We are given an ANOVA table with partial data and need to complete the table and calculate the F-statistic to test if diet affects weight gain in rats. 2. **Formulate hypotheses:** - Null hypothesis $H_0$: Diet has no significant effect on weight gain. - Alternative hypothesis $H_a$: Diet has a significant effect on weight gain. 3. **Given data:** - Between diets: $d.f = 2$, $SS = 280$ - Within diets: $d.f = 6$, $SS = 120$ - Total: $d.f = 8$, $SS = 400$ 4. **Calculate Mean Squares (MS):** - Mean Square Between Groups (MS_bg): $$MS_{bg} = \frac{SS_{bg}}{d.f_{bg}} = \frac{280}{2} = 140$$ - Mean Square Within Groups (MS_wg): $$MS_{wg} = \frac{SS_{wg}}{d.f_{wg}} = \frac{120}{6} = 20$$ 5. **Calculate F-statistic:** $$F = \frac{MS_{bg}}{MS_{wg}} = \frac{140}{20} = 7$$ 6. **Interpretation:** - The calculated $F$ value is 7. - Given critical $F_{crit} = 5.14$ for $d.f_{bg} = 2$ and $d.f_{wg} = 6$. - Since $F_{cal} = 7 > F_{crit} = 5.14$, we reject the null hypothesis $H_0$. 7. **Conclusion:** There is sufficient evidence to conclude that diet has a significant effect on weight gain in rats. **Note:** The original message had $MS_{wg} = 15$ and $F = 9.33$, but with $SS_{wg} = 120$ and $d.f_{wg} = 6$, $MS_{wg}$ should be $20$ and $F$ should be $7$.