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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2013/iii/paper-35/4/d/solution
Past exam of the mathematics course of the University of Cambridge 2013 iii Paper 35 4 d Solution by
Codex 0 Created 2026-10-03 Updated 2026-10-07
Report the six treatment-combination means and their uncertainty, together with useful marginal treatment contrasts, standard errors and confidence intervals. Means are needed to interpret direction and practical importance, while the fitted interaction term determines whether one factor's effects should be reported separately at levels of the other. For the pairwise marginal comparisons in part (c), ordinary model-based 95% Student t confidence intervals use times the corresponding standard error; a simultaneous set of comparisons needs an appropriate adjustment.
Also describe orchard selection, actual randomization, treatment delivery, numbers of trees observed, missing data and response units. Check orchard-level residuals for unequal variance, outliers or systematic patterns using a residual-versus-fitted plot and an appropriate distributional diagnostic. Explain that twelve orchards provide independent treatment replication; 360 tree measurements provide subsampling precision. No numerical treatment means or numerical confidence intervals can be recovered from the supplied sums of squares in ANOVA alone.
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