Question

please show work and explain steps

The following table shows the results of four samples from four different normal populations. Assume that it is suitable for the ANOVA Sample Sample Size Sample Mean Sample Variance А 6 54 95 B 6 64 30 C 72 75 D 6 55 6 The sample grand mean is 63. We want to test whether there are differences in the four population means at the 1% level of significance. What is the value of erroa mean square?

Answer 1

We know that, Error mean square = $\frac{SSE}{n-k}$

Now,

$SSE=\sum n_i\times S_{i}^2=6(95)+6(30)+6(75)+6(55)=1530$

So,

Error mean square = $\frac{SSE}{n-k}=\frac{1530}{(6+6+6+6)-4}=76.5$