(b) A new fitness programme is devised for people who would like to lose weight. Each participants' weight in kg was measured before and after the fitness program to see if it is effective in reducing their weights. The following data were obtained. Participant #1 #2 #3 #4 #5 #6 #7 #8 Before 86 65 74 55 93 52 66 67 After 81 62 71 49 83 51 61 63 i. Carry out an appropriate hypothesis test to determine whether the fitness programme is effective in reducing weight. State the test hypotheses, and specify your test statistic and its distribution under the null hypothesis. Comment on your findings. ii. State any assumptions you made in (i.). iii. State an alternative hypothesis test to determine whether the fitness pro- gramme is effective in reducing weight. Justify why you did not use this hypothesis test in part 4i. iv. Give a 95% confidence interval for the difference in means. v. On the basis of the data alone, would you consider trying this fitness programme if you wanted to lose weight? Provide an explanation with your