= Solution
The <analysis of variance> provides evidence of a chocolate effect both with day included ($F_{3,18}=3.9665$, <p-value> $0.02473$) and with day omitted ($F_{3,20}=4.039$, <p-value> $0.02133$). Because every chocolate–day cell has the same replication, <balanced factorial orthogonality> separates the two main effects; the chocolate row is meaningful despite being entered first.
The chocolate-only fitted group means are approximately $14.17,11.67,9.33,11.33$ boards for A, B, C, D respectively. Thus \b[A has the largest fitted lecturing speed and C the smallest]. Relative to A, the fitted differences are $-2.50,-4.83,-2.83$ boards. The printed individual <Student t-tests> give strong evidence for the A–C contrast (<p-value> $0.00245$); B and D versus A have <p-values> $0.08835$ and $0.05582$, respectively. Those latter contrasts are not significant at 5%, and the output does not test all other pairwise comparisons. Simultaneous claims would require accounting for <multiple hypothesis testing>.
There is little evidence of a day effect after adjusting for chocolate. A chocolate-only <normal linear model> is therefore a reasonable simpler summary, with residual <standard deviation> about $2.42$ boards and explained variation $R^2\simeq0.377$. This is an association under the additive <statistical model>; a causal claim would additionally require an appropriate assignment of chocolate and checks of the <regression residuals> and possible <interaction terms>.
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