Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 35 / 4 / f / ii / Solution

Allocate the extra orchards evenly, giving three independent orchards to each of the six combinations. Each orchard still has mean variance $8$ under the fitted model. Each pruning marginal now uses six orchards and each spray marginal nine, givingBoth are two-thirds of their original values. The orchard residual statistical degrees of freedom increase from $12-6=6$ to $18-6=12$.

Extra orchards improve independent replication, give a predicted one-third reduction in contrast variances, and improve error estimation. Both this option and using 45 trees require 540 tree measurements, but extra orchards offer the greater predicted statistical gain under the fitted model. They may cost more to recruit and administer; their suitability and comparability also matter.