378 42 Suppose the Total Sum of Squares for a completely randomzied design with $p = 4$ treatments and $n = 16$ total measurements (SS(Total))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) Sum of Squares for Treatment (SST) is $90$% of SS(Total)

$F =$

Rejection region $F >$
The final conclustion 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) Sum of Squares for Treatment (SST) is $50$% of SS(Total)

$F =$

Rejection region $F >$
The final conclustion 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) Sum of Squares for Treatment (SST) is $20$% of SS(Total)

$F =$

Rejection region $F >$
The final conclustion 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.