Module 4 project

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Apr 3, 2024

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C ASE S TUDY : 10000 M ETER RACE AT THE 2016 R IO O LYMPICS 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. Assume the populations are normally distributed. *Done on xcel but used my TI-83 to check 1. Use the samples to find the mean completion time of the for the (Stat>insert data>stats>calc>1-var stats> enter a. male runners. 27.955 b. female runners. 31.490 2. Use the samples to find the sample standard deviation of the completion times for the (Stat>insert data>stats>calc>1-var stats> enter a. male runners . 0.708 b. female runners. 0.960 3. Find a point estimate for the mean completion time of the (Stat>insert data>stats>calc>1-var stats> enter a. male runners. 27.955 b. female runners. 31.490 c. Construct a 95% confidence interval for the population mean completion time of the 946) 4. Interpret the results of number 4. (Stats>Test>1-propint>input data>calculate) a. male runners. (27.608,28.302) b. female runners. ( 31.034,31.946) 5. Interpret the results of number 4. (Stats>Test>1-propint>input data>calculate) 95% of male runners completion time lies between (27.608,28.302) 95% of female runners completion times lie between ( 31.034,31.946) 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. (Stats>Test>1- propzint>input data>calculate) a. (29.101,30.451) b. The confidence interval for overall runners is between the confidence interval male runners and female runners. 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 Z-Test: (Stats>Test>Z-test>input data>calculate)

a. male runners. Assume the population standard deviation is 0.64 minutes. My answer is: 43 b. female runners. Assume the population standard deviation is 1.12 minutes. My answer is: 143 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. a. The men’s mean competition time and the woman’s mean completion times are not the same. This is because the men’s completion lies between (27.608,28.302 whereas woman’s completion lies between (31.034,31.946) 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). a. Ho : μ Male≥μ female ( claim ) Ha : μ Male < μ female a. What type of test will you use? t-test b. Where is the rejection region? Right tailed test, 1.311 c. Find the critical value(s). α = 0.10 (invnorm: .10) 1.311 (stat>test>z-test>input data> calculate) d. What is the value of the standardized test statistic? -12.088 e. What is your p-value? 0.0000000000003 > 0.000 f. What is your decision? Reject H0 g. Write your conclusion. There is enough evidence to support the claim that the women’s mean completion time is greater than the men’s mean completion time. Country Women's Name Time in KEN Vivian Jepkemoi CHERUIYOT 29.54 USA Molly HUDDLE 30.22 AUS Eloise WELLINGS 31.25 SWE Sarah LAHTI 31.47 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 AUS David MCNEILL 27.86 RSA Stephen MOKOKA 27.91 BEL Bashir ABDI 28.03 UGA Moses Martin KURONG 28.06 ERI Goitom KIFLE 28.27 BRN El Hassan ELABBASSI 28.34 AUS Ben ST LAWRENCE 28.77 JPN Kota MURAYAMA 29.04 CAN Mohammed AHMED 29.55

NED Susan KUIJKEN 31.54 GBR Jessica ANDREWS 31.60 JPN Yuka TAKASHIMA 31.61 JPN Hanami SEKINE 31.74 CAN Natasha WODAK 31.89 UZB Sitora HAMIDOVA 31.96 POR Carla Salome ROCHA 32.10 NED Jip VASTENBURG 32.15 ITA Veronica INGLESE 32.20 MEX Brenda FLORES 32.65 GBR Beth POTTER 33.07

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Module 4 Project Answer Sheet – Use space to the right to show any work. 2. a. ______________________ (3 points) b. ______________________ (3 points) 3. a. ______________________ (3 points) b. ______________________ (3 points) 4. a. ______________________ (3 points) b. ______________________ (3 points) 5. a. ______________________ (5 points) b. ______________________ (5 points) 6. a. __________________________________________________________________ ________________________________________________________________ (3 pts) b. __________________________________________________________________ ________________________________________________________________ (3 pts) 7. a. ______________________ (8 points) b. ________________________________________________________________ (4pts) 8.

a. ______________________ (4pts) b. ______________________ (4pts) 9. __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ _______________________________________________________________ (6pts) 10. a. Ho: _________________ Ha: __________________ Label the claim. (6pts) b. What type of test will you use? (Z-Test, T-test, or 1-ProZTest) _______________ (4 pts) c. Where is the rejection region? (Left-tailed, Right-tailed, Two-tailed test) _______ (4 pts) d. Find the critical value(s). α = 0.10 ________________ (5 pts) e. What is the value of the standardized test statistic? _________________ (5 pts) f. What is your p-value? __________________ (5 pts) g. What is your decision? (Reject Ho or Fail to Reject Ho) _________________ (5 pts) h. Write your conclusion. There ____________ (is/is not) enough evidence to ______________ (support/reject) the claim that _________________. (6 points)