Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 30 / 2 / d

Test $H_0:{\gamma }_d=0$ for both nonreference days, against at least one nonzero day fixed effect, conditional on chocolate. There are two added regression coefficients and $24-6=18$ residual statistical degrees of freedom. The nested-model F-test statistic isUnder $H_0$ and the normal linear model assumptions, $F\sim F_{2,18}$. Its 5% upper critical value is $3.555$, so do not reject the absence of day effects; the p-value is approximately $0.456$. Thus the missing row has two statistical degrees of freedom, mean square $4.875$, and the F-test value above. These observations do not provide evidence that including day improves the chocolate-adjusted mean model. They do not prove that every possible day effect or chocolate–day interaction term is absent.