 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 isEach spray marginal sample mean uses six orchards. Similarly,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 $30^2$.