Question 2 (20 points) An article in the Journal of Sports Sciences [Iron Status in Winter Olympic Sports (1987, Vol. 5(3), pp. 261271)] presents the results of an investigation of the hemoglobin level of Canadian Olympic ice hockey players. The data reported are as follows (in g/ d1): 15.3,16.0,144,149,15.7,15.3,16.0,15.0,15.7,14.8, 14.6, 15.6, 16.2, 16.2, 14.6,15.7,16.2,14.7,14.5, 15.2. (a) (5 points) Given the following probability plot of the data, what is a logical assumption about the underlying distribution of the data? Pmba bility Plat Ordered values -2.|] 1.5 -1.0 -(].5 00 US LlJ 1.5 2.0 Theoretical quantlles (b) (5 points) Explain why this check of the distribution underlying the sample data is im portant if you want to construct a condence interval on the mean. (c) (5 points) Based on this sample data, constrcut a twosided 95% condence interval for the mean hemoglobin level. ((1) (5 points) Consider the hypothesis testing H0 : u = 14.9 g/dl, v.s. H1 : ,u a 14.9 g/dl. Using part (c), without performing hypothesis testing directly, argue whether H 0 should be rejected or not at o: = 0.05