15 12 19 18 13 17 17 16 16 17 17 13 14 11 18 14 10.6 12.6 13.35 13.5 13.55 12.9 11.8 13.05 13.4 12.05 11.05 11.8 11.8 11.9 12.35 12.5 11.95 12.9 11.6 12.2 10.2 11.95 11.75 11.75 9.4 11.5 9.8 9.75 10.15 10.95 6.8 10.25 13.25 12.5 13 10.6 12.65 11.45 12.55 12.8 10.8 10.6 13.2 9.95 10.15 9.7 10.15 10.35
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 2
The floor exercise is a commonly shared event between the Women’s and Men’s Artistic Gymnastics programs. Let’s compare the floor exercise scores of the female gymnasts and male gymnasts. To do this, we will consider the 2007, 2011, and 2015 results as sample data.
Part A: Individual All-Around Finals
We will first look at the floor exercise scores in the Individual Female All-Around Finals and in the Individual Male All-Around Finals.
i. Find the sample mean and sample standard deviation for the floor exercise scores in the Individual Female All-Around Finals.
ii. Find the sample mean and sample standard deviation for the floor exercise scores in the Individual Male All-Around Finals.
iii. Construct a 95% confidence interval for the difference in population mean floor exercise scores between female and male gymnasts in the Individual All-Around Finals. (Hint: Use the results of i. and ii. and use the t-distribution.)
iv. Using the confidence interval in part iii., can we infer at the 5% significance level that the population mean floor exercise score in the Individual All-Around Finals is different for female gymnasts and male gymnastics?
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