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
The floor exercise is a commonly shared
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.
| Female All-Around Finals Floor Exercise | Male All-Around Finals Floor Exercise |
| 15 | 13.55 |
| 14.85 | 13.75 |
| 15.2 | 13.5 |
| 14.25 | 14.25 |
| 13.85 | 13.35 |
| 13 | 13.85 |
| 13.6 | 13.5 |
| 13.7 | 13.1 |
| 14.05 | 12.8 |
| 12.7 | 12.35 |
| 14.05 | 13.25 |
| 13.65 | 10.6 |
| 13.25 | 12.6 |
| 13.25 | 13.35 |
| 13.55 | 13.5 |
| 12.95 | 13.55 |
| 13.55 | 12.9 |
| 13.05 | 11.8 |
| 11.85 | 13.05 |
| 13.2 | 13.4 |
| 11 | 12.05 |
| 13.8 | 11.05 |
| 12.25 | 11.8 |
| 12.1 | 11.8 |
| 12.1 | 11.9 |
| 11.6 | 12.35 |
| 11.9 | 12.5 |
| 12.05 | 12.35 |
| 10.75 | 11.95 |
| 11.2 | 12.05 |
| 10.55 | 11.6 |
| 11.1 | 10.9 |
| 10.45 | 12.5 |
| 9.6 | 12.05 |
| 13.85 | 13 |
| 14.25 | 13.6 |
| 14.8 | 13.8 |
| 14 | 12.55 |
| 14.5 | 12.8 |
| 13.75 | 12 |
| 13.55 | 13.5 |
| 12.55 | 12.05 |
| 13.2 | 13.15 |
| 13.7 | 13.25 |
| 13.35 | 11.8 |
| 13.25 | 12.75 |
| 12.95 | 12.35 |
| 13.4 | 12.75 |
| 13.35 | 12.2 |
| 13.3 | 12.85 |
| 12.3 | 12.45 |
| 13.55 | 12.7 |
| 12.8 | 12.55 |
| 12.4 | 12.35 |
| 13.1 | 12.25 |
| 12.3 | 12.45 |
| 12.6 | 13 |
| 12.65 | 12.05 |
| 11.9 | 12 |
| 10.2 | 12.5 |
| 12.05 | 12.2 |
| 11.7 | 12.25 |
| 10.4 | 11.85 |
| 10.75 | 11.95 |
| 9.8 | 11.5 |
| 9.6 | 11.5 |
| 10.75 | 9.7 |
| 9.75 | 10.55 |
| 9.55 | 10 |
| 9.05 | 12.1 |
| 14.65 | 12.85 |
| 14.2 | 12.65 |
| 15.35 | 12.9 |
| 14.6 | 11.8 |
| 14.3 | 12.9 |
| 14.75 | 12.45 |
| 13.65 | 11.95 |
| 13.7 | 12.1 |
| 14.25 | 11.8 |
| 13.8 | 12.35 |
| 14.1 | 12.1 |
| 13.6 | 12 |
| 14 | 11.85 |
| 14.25 | 12.2 |
| 13.2 | 11.7 |
| 14.4 | 12.15 |
| 13.25 | 11.3 |
| 13.7 | 11.3 |
| 13.15 | 12.4 |
| 13.05 | 12 |
| 13.45 | 12 |
| 12.4 | 11.45 |
| 13.3 | 11 |
| 12.75 | 10.85 |
| 12.2 | 11.25 |
| 12.6 | 10.6 |
| 11.55 | 10.5 |
| 11.6 | 10.1 |
| 11.6 | 11 |
| 10 | 11 |
| 10.9 | 10.85 |
| 10.35 | 10.35 |
| 11.75 | 10.2 |
| 11.3 | 11.05 |
| 10.3 | |
| 10.9 |
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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