Supplementary Exercise 12.40 of IPS7e
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(a) The null hypothesis is that the three population means are equal,
not the three sample means. Hypotheses are always about parameters in
the relevant population(s). No test is needed to determine whether
sample means are different or not because we can simply look at the 
values and decide which is true.


(b) It is *not* true that the mean squares add up. The degrees of
freedom and the sum of squares columns add up, but that is not the case
for mean squares.


(c) The within-group variation is the variation from the mean in each group,
and therefore this variation is unrelated to mean differences. By contrast,
the mean differences are quantified in the between-group variation.