I want you to solve all part a, b, and c. Also, you should show me all your solutions step by step. You should use R program and give me all your codes.

Problem 14.4 Thirty consumers are asked to rate the softness of clothes washed by ten different detergents, but each consumer rates only four different detergents. The design and responses are given below: Trts Softness 1 A B C D 37 23 37 41 2 A BEF 35 32 39 37 3 A CGH 39 45 39 41 4 AD I J 44 42 46 44 5 AEG I 44 44 45 50 6 AFHJ 55 45 53 49 7 BCF I 47 50 48 52 8 BDG J 37 42 40 37 9 BEH J 32 34 39 29 10 BGH I 36 41 39 43 11 CE I J 45 44 40 36 12 CFGJ 42 38 39 39 13 CD EH 47 48 46 47 14 D E F G 43 47 48 41 15 D FH I 39 32 32 31 Trts Softness 16 ABCD 52 41 45 48 17 A BEF 46 42 45 42 18 ACGH 44 43 41 36 19 AD I J 32 42 36 29 20 AEG I 43 42 44 44 21 A FH J 46 41 43 45 22 43 51 40 42 23 BDG J 38 37 36 34 24 40 49 43 44 25 BGH I 23 20 27 29 26 CE I J 46 49 48 43 27 CFG J 48 43 48 41 28 CD EH 35 35 31 26 29 D E F G 45 47 47 42 30 D FH I 43 39 38 39 1. Do problem 14.4 on p.382 of our text. In answering this problem, complete the following steps. a. What are the values of r, k, b, a and for this design? . b. Analyze these data. State the model that you use, present the ANOVA Table, test for main effects of detergents, and compare detergents A and B with detergents C, D, and E. State your conclusions. c. In a situation like this, it is often of interest to pick the winner. What is the best detergent (the detergent that produces the highest softness ratings)? Which detergents have significantly lower mean softness ratings than the best detergent? To answer this question, the best approach is to use Dunnett's procedure for multiple comparisons with the best treatment. Problem 14.4 Thirty consumers are asked to rate the softness of clothes washed by ten different detergents, but each consumer rates only four different detergents. The design and responses are given below: Trts Softness 1 A B C D 37 23 37 41 2 A BEF 35 32 39 37 3 A CGH 39 45 39 41 4 AD I J 44 42 46 44 5 AEG I 44 44 45 50 6 AFHJ 55 45 53 49 7 BCF I 47 50 48 52 8 BDG J 37 42 40 37 9 BEH J 32 34 39 29 10 BGH I 36 41 39 43 11 CE I J 45 44 40 36 12 CFGJ 42 38 39 39 13 CD EH 47 48 46 47 14 D E F G 43 47 48 41 15 D FH I 39 32 32 31 Trts Softness 16 ABCD 52 41 45 48 17 A BEF 46 42 45 42 18 ACGH 44 43 41 36 19 AD I J 32 42 36 29 20 AEG I 43 42 44 44 21 A FH J 46 41 43 45 22 43 51 40 42 23 BDG J 38 37 36 34 24 40 49 43 44 25 BGH I 23 20 27 29 26 CE I J 46 49 48 43 27 CFG J 48 43 48 41 28 CD EH 35 35 31 26 29 D E F G 45 47 47 42 30 D FH I 43 39 38 39 1. Do problem 14.4 on p.382 of our text. In answering this problem, complete the following steps. a. What are the values of r, k, b, a and for this design? . b. Analyze these data. State the model that you use, present the ANOVA Table, test for main effects of detergents, and compare detergents A and B with detergents C, D, and E. State your conclusions. c. In a situation like this, it is often of interest to pick the winner. What is the best detergent (the detergent that produces the highest softness ratings)? Which detergents have significantly lower mean softness ratings than the best detergent? To answer this question, the best approach is to use Dunnett's procedure for multiple comparisons with the best treatment