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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 in any Apparatus Finals |
Competed in exactly one Apparatus Finals event | Competed in more than one Apparatus Finals event | |
|
Did not win team medal |
66 | 10 | 7 |
| Won team medal | 10 | 13 | 13 |
a) A Canada Games gymnast is chosen at random. What is the probability that they did not win a team medal or did not compete in any Apparatus Finals event?, what is the probability that they competed in more than one Apparatus Finals event given that they won a team medal? and what is the probability that they won a team medal and competed in at least one Apparatus Final event?
b) Test at the 5% significance 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 Z2 test of independence.)
c) For gymnasts who did not win a team medal, construct 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 and for gymnasts who won a team medal, construct 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. Closely examine both pie charts. 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?).
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