1. Genetically identical seeds are randomly assigned to be raised either under normal conditions or in one of two types of nutritionally enriched environment. The results of a balanced experiment to compare yield sizes, as measured by the dried weights (in grams) of 10 plants in each setting, are summarised below: Control 4.17 5.58 5.18 6.11 4.17 4.61 5.17 4.53 5.33 5.14 Treatment A 4.81 4.17 4.41 3.59 5.87 3.83 6.03 4.89 4.32 4.69 Treatment B 6.31 5.12 5.54 5.50 5.37 5.29 4.92 6.15 5.80 5.26 A researcher conducts a Kruskal-Wallis test to compare yield size across groups and asks you to verify their work. NOTE: tables of relevant critical values and a formula needed for part (b) are provided in the final pages of this exam script. (a) State the assumptions underpinning the Kruskal-Wallis test. [6 marks] (b) The researcher obtained a test statistic of 7.719 for the Kruskal-Wallis test they performed, without applying an adjustment to account for tied ranks. Verify this value by hand and show your workings. [9 marks] (c) Perform a tie-adjustment to the test statistic from part (b). You should find a value of 7.726 but must show your workings by hand. [3 marks] (d) State clearly the null and alternative hypotheses of such a test and also give your conclusion, with reference to an appropriate critical value from the tables at the end of this exam script. Use a = 0.05. [6 marks] (e) The researcher subsequently performs pairwise two-sided Wilcoxon-Mann- Whitney tests and gathers some of the output they obtained in the table below, where X denotes the first group in the comparison: Group X Wx U p-value Group Y Treatment A 120 35 0.2723 Control Control 80 25 0.0639 Treatment B Treatment B Treatment A 71 16 0.0089 No adjustment for multiple comparisons is included in the output above. Interpret the above tests, but include a Bonferroni adjustment. [5 marks] (f) Given Wx 71, verify the value of the test statistic U = 16 for the Treatment A vs. Treatment B comparison in the table of output above by hand. Show your workings. [5 marks]