QUESTION 2. Two factor experiment [15 marks] (a) Construct a single chart that displays twelve boxplots, one for each combination of factor levels [2 marks] . Of the three assumptions the F -tests from two-way ANOVA rely on, which is most called into question by these plots [1 mark] ? (b) Write down the statistical model for a 2 x6 completely randomised block design consistentwith the sample data, excludinginteraction between the factors [2 marks] . Identify the treatments [1 marks] . (c) Using significance level =0.05 , perform two-way ANOVA (without interaction) and document the F -test for the blocking factor only (marks will be deducted for documenting additional F -tests other than this). Write down the null and alternative hypotheses, the test statistic and p-value, the test decision with reason and a conclusionusing a minimum of mathematicallanguage [3 marks] . (d) Using significance level =0.05 , perform Tukey post-hoc analysis to determine which pairs of plot groups are associated with different mean yield of peas [3 marks] . (e) Using diagnostic plots of the residuals, assess whether the assumptions underpinningthe F -test conducted above have been met [3 marks]