Question 4

Question 4 The organizers of the Canada Games are interested to know whether there is any association between a gymnast winning a team medal and the number of Apparatus Finals competitions in which they compete. A team medal winner is a gymnast whose team placed in the top 3 in the Team Competition. Consider the following table summarizing the number of gymnasts who competed in the 2015 Canada Games- Did not compete Competed in Competed in in any exactly one more than one Apparatus Apparatus Apparatus Finals event Finals event Finals event n team medal medal a] A Canada Games gymnast is chosen at random. What is the probability that they i. did not win a team medal or did not compete in any Apparatus Finals event? ii. competed in more than one Apparatus Finals event given that they won a team medal? iii. won a team medal and competed in at least one Apparatus Final event? b} Test at the 5% signicance level the claim that a gymnast winning a team medal is independent of the number of Apparatus Finals events in which they compete. (Hint: Use the x2 test of independence-) c} For gymnasts who did not win a team medal, constnIct a pie chart indicating the proportion of gymnasts who competed in no Apparatus Finals event, exactly one Apparatus Finals event, and more than one Apparatus Finals event. d} For gymnasts who won a team medal, constant a pie chart indicating the proportion of gymnasts who competed in no Apparatus Finals event, exactly one Apparatus Finals event, and more than one Apparatus Finals event. e} Closely examine the pie charts in part c} and part d}. Do these pie charts support the results of the hypothesis test in part b}? Explain. (Hint: How would the appearance of the pie charts differ from those constructed if winning a team medal was independent of the number of apparatus finals?)