2.Three different washing machines were employed to test four different detergents. Thefollowing data give a coded score of the effectiveness of each washing. Machine Detergent 1 2 3 1 5a 50 5a 2 54 54 50 3 55 58 52 4 5o 45 5? (a) Give the two-way ANDVA 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 tomachine (i) l and (ii) 2. (d) Test the hypodiesis that the detergent used does not affect the score, at the 5 percentlevel of significance. (e) Test the hypothesis that the machine used does not affect the score, at the 5 peroentlevel 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