2. Three different washing machines were employed to test four different detergents. The following data give a coded score of the effectiveness of each washing. Machine Detergent 1 2 3 53 50 59 54 60 C N - 54 56 58 62 50 45 57 (a) Give the two-way ANOVA table based on the data. (b) Estimate the improvement in mean value with detergent 1 over detergent (i) 2, (ii) 3, and (iii) 4. (c) Estimate the improvement in mean value when machine 3 is used as opposed to machine (i) 1 and (ii) 2. (d) Test the hypothesis that the detergent used does not affect the score, at the 5 percent level of significance. (e) Test the hypothesis that the machine used does not affect the score, at the 5 percent level of significance. (f) Suppose that the 12 applications of the detergents were all on different randomly chosen machines. Test the hypothesis, at the 5 percent significance level, that the detergents are equally effective