METER RACE AT THE 2016 RIO OLYMPICS

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CASE STUDY: 10000 METER RACE AT THE 2016 RIO OLYMPICS
In 10000 meter race, runners complete over 25 laps or 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 2016 Rio 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, do not use their
data.
1. Use the samples to find the mean completion time of the for the
a. male runners.
b. female runners.
2. Use the samples to find the sample standard deviation of the completion times for the
a. male runners.
b. female runners.
3. Find a point estimate for the mean completion time of the
a. male runners.
b. female runners.
4. Construct a 95% confidence interval for the population mean completion time of the
a. male runners.
b. female runners.
5. Interpret the results of number 4.
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.
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 0.64 minutes.
b. female runners. Assume the population standard deviation is 1.12 minutes.
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.
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).

Sample Solution

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