a) Ten hamsters were selected for a nutritional experiment. Each hamster's weight were recorded in grams and divided into two different groups. The first group of hamsters was fed with Formula A while the second group of hamsters was fed with Formula B. At the end of a specified time period, each hamster was weighed again and the net weight gained in grams was recorded. Assume that the net weight gained of hamsters is normally distributed. Formula A 43.5 39.4 41.3 46 38.2 Formula B 51.2 40.9 37.9 45 48.6 The Minitab output is shown below. Test and Cl for Two Variances: Formula A, Formula B Statistics Sample N StDev Variance Formula A 3. 1396 9. 8571 Formula B 5 5. 4366 29.5566 Tests Method DF1 DF2 Test Statistic P-Value F 4 4 0. 3335 0 . 3127 i) Are the two groups of hamsters independent samples? Explain your answer. (2 marks) ii) At a 10% level of significance, can it be concluded that the two groups of hamsters have different population variances in weight gained? (4 marks) iii) From your conclusion in (ii), test at 10% significance level whether formula B has resulted in more mean weight gained compared to formula A. (7 marks) iv) State whether the test in (iii) is a Type I or Type II error. Explain your answer in the context of this problem. (2 marks)