= Solution
The reduced model combines the 0-, 3-, and 6-point categories. Relative to the full model, the null hypothesis is $\eta_3=\eta_6=0$, leaving the 9-point contrast unrestricted. These are two linear restrictions on an otherwise unchanged <normal linear model>.
For nested normal models, the reduction in <residual sum of squares> divided by $\sigma^2$ has a <chi-squared distribution> with degrees of freedom equal to the number of restrictions. It is independent of the full model's residual variance estimate. Hence the <F-test> statistic is
$$
F=\frac{(22323-19512)/2}{19512/24}=1.728782\sim F_{2,24}\quad\text{under }H_0.
$$
It is below the supplied 5% critical value $3.402826$, so \b[do not reject equal effects for 0, 3, and 6 points]. There is insufficient evidence that separating those categories improves this additive model; this does not prove that their true premiums are identical.
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