2. We wanted to compare 4 diets with regard to the average weight (in kg) that they allow you to lose. The study was designed as a completely randomized design. The following data were obtained from random samples on each of these methods: Diet 1 Diet 2 Diet 3 Diet 4 4.8 8.7 9.6 7.9 7.1 7.7 2.1 4.2 5.4 4.1 6.7 3.1 8.6 6.3 8.5 5.7 1.7 2.8 3.6 5.52 5.92 6.725 4.9 mean 2.6033 2.454 3.3069 1.9404 std. dev. The global mean was 5.7157 kg and the global std. dev. is 2.43659 kg. (a) Formulate the hypotheses (i.e. give Ho and Ha) to be tested in the case of the test for the significance of the treatment effects. (b) Complete the corresponding ANOVA table. (c) Compute the p-value with R and give the conclusion of the test for the significance of the treatment effects at a = 5%. (d) Consider the family of all pairwise comparisons. How many comparisons are there? (e) We will use the Tukey method for the family of all pairwise comparisons with a = 5%. For this family of comparisons, compute the adjusted confidence interval for and the adjusted p-value for comparing diets 1 and 2. Can we conclude that diets 1 and 2 are honestly significantly different? (f) We will use the Tukey method for the family of all pairwise comparisons with a = 5%. For this family of comparisons, compute the adjusted confidence interval for -4 and the adjusted p-value for comparing diets 3 and 4. Can we conclude that diets 3 and 4 are honestly significantly different?