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Four friends decided to compare three brands of ski for speed down their favourite ski slope. Each person did two runs with each brand of ski, and their times in seconds are recorded below. f. [6 marks] Output for a two-way ANOVA is presented on page 12 of the Reference Booklet. Using a 5% significance level, do as many tests from the ANOVA table as are appropriate. For each test, give the null and alternative hypotheses, then the p-value and your statistical conclusion. (Here, you may assume that the assumptions of ANOVA are met.) g. [5 marks] A Tukey test for ski brand is given on page 12 of the Reference Booklet. Based on the results of part (f), is it valid to use this Tukey test? If not, explain why not. If so, briefly summarise the Tukey results. (As in part (f), you may assume that the assumptions of ANOVA are met.) Two-way ANOVA 38.83 12.94 101 .33 50.67 78.67 13.11 4.75 2-1 3-1 3-2 Sum 57. Sq 00 Mean factor (person) factor (brand) Residuals Signif. codes : Df 3 2 factor (person) : factor (brand) 6 12 Sq F value 2.725 10.667 2.760 0.05 o. 09067 0.00218 o. 06348 o 0.001 0.01 Tukey multiple comparisons of means 95% familyvise confidence level Fit: aov(formula = time factor(brand)) $ s factor (brand) diff 3 5 2 Ivr -o .6329287 1 .3670713 -1.6329287 upr 5 .632929 6.632929 0.1180027 8.632929 0.0062194 p adj o .3651379