Suppose the Total Sum of Squares (SST) for a completely randomzied design with $k = 4$ treatments and $n = 16$ total measurements is equal to $420$. In each of the following cases, conduct an $F$-test of the null hypothesis that the mean responses for the $4$ treatments are the same. Use $\alpha = 0.1$.

(a) The Treatment Sum of Squares (SSTR) is equal to $378$ while the Total Sum of Squares (SST) is equal to $420$.

The test statistic is$F =$

The critical value is $F =$

The final conclusion is:
A. There is not sufficient evidence to reject the null hypothesis that the mean responses for the treatments are the same.
B. We can reject the null hypothesis that the mean responses for the treatments are the same and accept the alternative hypothesis that at least two treatment means differ.

(b) The Treatment Sum of Squares (SSTR) is equal to $210$ while the Total Sum of Squares (SST) is equal to $420$.

The test statistic is $F =$

The critical value is $F =$

The final conclusion is:
A. There is not sufficient evidence to reject the null hypothesis that the mean responses for the treatments are the same.
B. We can reject the null hypothesis that the mean responses for the treatments are the same and accept the alternative hypothesis that at least two treatment means differ.

(c) The Treatment Sum of Squares (SSTR) is equal to $84$ while the Total Sum of Squares (SST) is equal to $420$.

The test statistic is$F =$

The critical value is $F =$

The final conclusion is:
A. There is not sufficient evidence to reject the null hypothesis that the mean responses for the treatments are the same.
B. We can reject the null hypothesis that the mean responses for the treatments are the same and accept the alternative hypothesis that at least two treatment means differ.