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Fayetteville State University *
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Statistics
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Apr 3, 2024
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docx
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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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