Suppose the Total Sum of Squares (SST) for a completely randomzied design with $k = 6$ treatments and $n = 30$ total measurements is equal to $460$. In each of the following cases, conduct an $F$ -test of the null hypothesis that the mean responses for the $6$ treatments are the same. Use $\alpha = 0.1$.

(a) The Treatment Sum of Squares (SSTR) is $80$% of the Total Sum of Squares (SST)

The test statistic is$F =$

The critical value is $F =$

The final conclusion is

(b) The Treatment Sum of Squares (SSTR) is $70$% of the Total Sum of Squares (SST)

The test statistic is $F =$

The critical value is $F =$

The final conclusion is

(c) The Treatment Sum of Squares (SSTR) is $30$% of the Total Sum of Squares (SST)

The test statistic is$F =$

The critical value is $F =$

The final conclusion is

Your overall score for this problem is