Gymnastics Case Study The Canada Games represents the highest level of national competition for up and coming Canadian athletes. Alternating between winter and summer, the competition is held once every two years. Niagara will be the proud host of the 2022 Canada Summer Games. In this case study, your group will explore the athletes’ information and achievements as given in the “Gymnastics” data sheet to make summaries and inferences. Gymnastics Events Artistic gymnastics has been part of the Canada Winter Games since the inaugural Games in 1967 in Quebec City and features both Men’s and Women’s competition. Women's Artistic Gymnastics Apparatus Events Men's Artistic Gymnastics Apparatus Events Vault Uneven bars Beam Floor Floor Pommel horse Rings Vault Parallel bars Horizontal bars Team Competition Each team consists of 6 athletes from the same province/territory. Each athlete competes on every apparatus. The best 4 scores in each apparatus are added together for the team score. Individual All-Around Finals The top 3 gymnasts per province/territory from the Team Competition competes in the Individual All-Around Finals, with a total of up to 36 participants based on scores obtained in the preliminary competition. Each athlete competes on every apparatus. The scores in each apparatus are added together for the individual score. Apparatus Finals The top 8 gymnasts in each event (with a maximum of 2 per province/territory) from the Team Competition will compete in the Apparatus Finals Competition. 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 in any Apparatus Finals event 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 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?
Gymnastics Case Study
The Canada Games represents the highest level of national competition for up and coming Canadian athletes. Alternating between winter and summer, the competition is held once every two years. Niagara will be the proud host of the 2022 Canada Summer Games. In this case study, your group will explore the athletes’ information and achievements as given in the “Gymnastics” data sheet to make summaries and inferences.
Gymnastics Events
Artistic gymnastics has been part of the Canada Winter Games since the inaugural Games in 1967 in Quebec City and features both Men’s and Women’s competition.
|
Women's Artistic Gymnastics Apparatus Events |
Men's Artistic Gymnastics Apparatus Events |
|
Vault Uneven bars Beam Floor |
Floor Pommel horse Rings Vault Parallel bars Horizontal bars |
Team Competition
Each team consists of 6 athletes from the same province/territory. Each athlete competes on every apparatus. The best 4 scores in each apparatus are added together for the team score.
Individual All-Around Finals
The top 3 gymnasts per province/territory from the Team Competition competes in the Individual All-Around Finals, with a total of up to 36 participants based on scores obtained in the preliminary competition. Each athlete competes on every apparatus. The scores in each apparatus are added together for the individual score.
Apparatus Finals
The top 8 gymnasts in each
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 in any Apparatus Finals event | 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
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% 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 ?2 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.
d) 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.
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?)
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