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Male and Female Runners

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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.

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. Assume the populations are normally distributed.

1. Use the samples to find the mean completion time of 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.
a. __________________________________________________________________
________________________________________________________________
b. __________________________________________________________________
________________________________________________________________

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.

a. ______________________
b. ______________________________________________________________________
_________________________________________________________________

7. 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.

__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
_______________________________________________________________

8. 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 from 1a).

a. Ho: _________________ Ha: __________________ Label the claim.
b. What type of test will you use? (Z-Test, T-test, or 1-ProZTest) _______________
c. Where is the rejection region? (Left-tailed, Right-tailed, Two-tailed test) _______
d. Find the critical value(s). α = 0.10 ________________
e. What is the value of the standardized test statistic? _________________
f. What is your p-value? __________________
g. What is your decision? (Reject Ho or Fail to Reject Ho) _________________
h. Write your conclusion.
There ____________ (is/is not) enough evidence to ______________ (support/reject) the claim that _________________.

9. A trainer decides to do a study because he wants to estimate the population mean completion times for both male and female runners within 1/4 minute (0.25 minute). How many runners of each sex does he need for his study? 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. ______________________

 

Country Men's Name Time in Minutes
KEN Paul Kipngetich TANUI 27.09
ETH Yigrem DEMELASH 27.11
UGA Joshua Kiprui CHEPTEGEI 27.17
ERI Zersenay TADESE 27.40
BRN Abraham Naibei CHEROBEN 27.53
NZL Zane ROBERTSON 27.56
USA Leonard Essau KORIR 27.59
TUR Polat Kemboi ARIKAN 27.59
ETH Abadi HADIS 27.61
JPN Suguru OSAKO 27.87
USA Shadrack KIPCHIRCHIR 27.97
PER Luis OSTOS 28.03
UGA Timothy TOROITICH 28.08
GBR Andrew VERNON 28.32
BDI Olivier IRABARUTA 28.55
JPN Yuta SHITARA 28.92
GBR Ross MILLINGTON 29.25

Country Women's Name Time in minutes
KEN Vivian Jepkemoi CHERUIYOT 29.54
KEN Alice Aprot NAWOWUNA 29.89
USA Molly HUDDLE 30.22
ETH Gelete BURKA 30.45
AUS Eloise WELLINGS 31.25
SWE Sarah LAHTI 31.47
BDI Diane NUKURI 31.48
GBR Joanne PAVEY 31.56
GRE Alexi PAPPAS 31.60
KGZ Darya MASLOVA 31.62
RSA Dominique SCOTT 31.86
UAE Alia Saeed MOHAMMED 31.95
CAN Lanni MARCHANT 32.07
RWA Salome NYIRARUKUNDO 32.13
ESP Trihas GEBRE 32.16
BRA Tatiele Roberta DE CARVALHO 32.64
USA Marielle HALL 32.66
MEX Marisol ROMERO 35.55

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The Excel file contains all the formulas, functions and calculations for the questions. The Word file compiles all the solutions from Excel.

Solution provided by:
J Pye, MSc
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  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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