= Solution
The orchard residual <mean square in ANOVA> is on the original tree-response scale: it equals 30 times the corresponding residual <mean square in ANOVA> for orchard means. Thus the estimated <variance> of one orchard's <sample mean> is $240/30=8$.
Each pruning marginal <sample mean> averages four independent orchard means, giving <variance> $8/4=2$. Two different pruning marginals use disjoint orchards, so the <variance> of their estimated <treatment contrast> is
$$
\boxed{\widehat{\operatorname{Var}}(\widehat\mu_{P_i}-\widehat\mu_{P_j})=2\frac{240}{30\cdot4}=4.}
$$
Each spray marginal <sample mean> uses six orchards. Similarly,
$$
\boxed{\widehat{\operatorname{Var}}(\widehat\mu_S-\widehat\mu_{\mathrm{no\ spray}})=2\frac{240}{30\cdot6}=\frac83.}
$$
The corresponding <standard errors> are $2$ and $\sqrt{8/3}$ in the units of weight per tree. These compare per-tree marginal <sample means>, averaging equally over the other factor, even when an <interaction term> is fitted. Comparing orchard totals instead would multiply these <variances> by $30^2$.
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