Module 4 project
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Statistics
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Jan 9, 2024
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docx
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C
ASE
S
TUDY
: 10000 M
ETER
RACE
AT
THE
2020 T
OKYO
O
LYMPICS
In the 10000-meter race, runners complete over 25 laps on a 400 meter track. It is the longest track running event held. The men’s 10000 meter began at the 1912 Olympics. It was 1988 (over seventy years later) before the women’s 10000 meter was added to Olympic competition. The official world records in the 10,000 meters are held by Kenenisa Bekele with 26:17.53 minutes for men and Almaz Ayana from Ethiopia with 29:17.45 minutes for women. In this project, we are going to take a look at the 2020 Tokyo Olympics men and women 10000-meter
competition. All the times for the participant’s times are given to you in minutes. You should leave the times in minutes and round to the nearest thousandth when needed. If the runner did not finish or disqualified, do not include their data.
1.
Use the samples to find the mean completion time of the for the
a.
male runners. 29:59.26 minutes
b.
female runners. 31:18.08 minutes 2.
Use the samples to find the sample standard deviation of the completion times for the
a.
male runners. 0.86 minutes
b.
female runners. 1.11 minutes
3.
Find a point estimate for the mean completion time of the
a.
male runners. 29:59.26 minutes
b.
female runners. 31:18.08 minutes
4.
Construct a 95% confidence interval for the population mean completion time of the
a.
male runners. 29:33.51 minutes to 30:25.01 minutes b.
female runners. 30:58.50 minutes to 31:77.66 minutes 5.
Interpret the results of number 4.
The 95% confidence intervals for both the male and female runners do not overlap, indicating that there
is a statistically significant difference in the mean completion times between the two groups. The mean completion time for male runners is approximately 1.59 minutes faster than the mean completion time for female runners.
6.
Use the samples to construct a 95% confidence interval for the population mean completion time of all runners. How do your results differ from those in number 4? Explain.
Mean completion time: 30:38.67 minutes
Sample standard deviation: 1.07 minutes
Confidence interval 30:12.28 minutes to 30:65.06
The 95% confidence interval for all runners is wider than the confidence intervals for the male and female runners separately. This is because the sample size for all runners is smaller than the sample sizes for the male and female runners separately.
7.
A trainer wants to estimate the population mean completion times for both male and female runners within 1/4 minute (0.25 minute). Determine the minimum sample size required to construct a 99% confidence interval for the population mean completion times of
a.
male runners. Assume the population standard deviation is 0.63 minutes. 12 b.
female runners. Assume the population standard deviation is 1.11 minutes. 25
8.
Based on the 95% confidence intervals found in number 4, do you think that the men’s mean completion time and the women’s mean completion time could be the same? Explain why you believe that.
Based on the 95% confidence intervals, it is unlikely that the men's mean completion time and the women's mean completion time could be the same. This is because the confidence intervals do not overlap.
9.
Using the values that you found in numbers 1 and 2, perform the following hypothesis test.
At a 10% significance level, test the claim that the women’s mean completion time is greater than ___________ (the men’s mean completion time).
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