Module 4 project 1

docx

School

Fayetteville State University *

*We aren’t endorsed by this school

Course

202

Subject

Statistics

Date

Apr 3, 2024

Type

docx

Pages

Uploaded by SSSSSMD

C ASE S TUDY : 10000 M ETER RACE AT THE 2016 R IO O LYMPICS *My answers are better organized under each paragraph but also placed on the answer sheet! 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 Men's Name Time in Minutes GBR Mohamed FARAH 27.09 ETH Tamirat TOLA 27.11 USA Galen RUPP 27.15 KEN Bedan Karoki MUCHIRI 27.38 ERI Nguse AMLOSOM 27.51 KEN Geoffrey Kipsang KAMWOROR 27.53 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 ETH Almaz AYANA 29.29 ETH Tirunesh DIBABA 29.71 KEN Betsy SAINA 30.13 TUR Yasemin CAN 30.44 NOR Karoline Bjerkeli GROVDAL 31.24 USA Emily INFELD 31.45 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 Module 4 Project Answer Sheet – Use space to the right to show any work. 2. a. _____ 27.955 ___________ (3 points) b. ______ 31.490 ________ (3 points) 3. a. ______ 0.708 _________ (3 points) b. _____ 0.960 _______ (3 points) 4.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

a. ______ 27.955 _________ (3 points) b. ______ 31.490 __________ (3 points) 5. a. _______ (27.608,28.302) ______ (5 points) b. _______( 31.034,31.946) _____ (5 points) 6. a. 95% of male runners completion time lies between (27.608,28.302) (3 pts) b. 95% of female runners completion times lie between ( 31.034,31.946) (3 pts) 7. a._______ (29.101,30.451) ____ (8 points) a. The confidence interval for overall runners is between the confidence interval male runners and female runners. (4pts) 8. male runners. Assume the population standard deviation is 0.64 minutes. My answer is: 43 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 (6pts) 9. 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 b. woman’s completion lies between (31.034,31.946) 10. Ho : μ Male≥μ female ( claim ) Ha : μ Male < μ femal a. Ho: _________________ Ha: __________________ Label the claim. (6pts)

b. What type of test will you use? (Z-Test, T-test, or 1-ProZTest) ___ t-test ___ (4 pts) c. Where is the rejection region? (Left-tailed, Right-tailed, Two-tailed test) _ Right tailed test, 1.311 ___ (4 pts) d. Find the critical value(s). α = 0.10 ___ (invnorm: .10) 1.311 ______ (5 pts) e. What is the value of the standardized test statistic? __ -12.088 _____ (5 pts) f. What is your p-value? ______ Reject H0 ____ (5 pts) g. What is your decision? (Reject Ho or Fail to Reject Ho) _____ Reject H0 ______ (5 pts) h. Write your conclusion. i. There is enough evidence to support the claim that the women’s mean completion time is greater than the men’s mean completion time. There ____enough_____ (is/is not) enough evidence to ______support______ (support/reject) the claim that ____woman’s mean completion time is greater than the med’s mean completion time.___________. (6 points)

Related Documents

Assignment 3 (5%).pdf

Assignment 4 (5%).pdf

L02 Quiz_ Homework_ Social Science Statistics.pdf

Untitled document (24).docx

Untitled document (19) (1).docx

Module 4 project.docx

8.4_Practice.pdf

Math Project 2.docx

Math DB 3.docx

Quiz 6 Working Papers.doc

Statistics Quiz practice.pdf

MAE301_HW8.pdf

Recommended textbooks for you

Holt Mcdougal Larson Pre-algebra: Student Edition...

Algebra

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Glencoe Algebra 1, Student Edition, 9780079039897...

Algebra

ISBN:9780079039897

Author:Carter

Publisher:McGraw Hill

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:9781133382119

Author:Swokowski

Publisher:Cengage

Algebra: Structure And Method, Book 1

Algebra

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:McDougal Littell

Mathematics For Machine Technology

Advanced Math

ISBN:9781337798310

Author:Peterson, John.

Publisher:Cengage Learning,

SEE MORE TEXTBOOKS

Recommended textbooks for you

Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,