Chapter 14.1, Problem 16E

Samples were drawn from three populations. The sample sizes were $n_1=9,n_2=7,n_3=10,n_4=8$. The sample means were $\overline{x_1}=73.5$, $\overline{x_2}=74.8$, $\overline{x_3}=78.2$. The sample standard deviations were $S_1=2.5,S_2=4.5,S_3=3.8,S_4=3.2$. The grand mean was $\bar{x}=75.34$.

1. Compute the sums of squares SSTr and SSE.
2. How many degrees of freedom are there for SSTr and SSE?
3. Compute the mean squares MSTr and MSE.
4. Compute the value of the test statistic F.
5. Can you conclude that two or more of the population means are different? Use the $\alpha =0.01$ level of significance.