Use the samples to find the mean completion time of the for the male runners. female runners. Use the samples to find the sample standard deviation of the completion times for the male runners. female runners. Find a point estimate for the mean completion time of the male runners. female runners. Construct a 95% confidence interval for the population mean completion time of the male runners. female runners. Interpret the results of number 4. 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. 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. 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 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 male runners. Assume the population standard deviation is 0.64 minutes. female runners. Assume the population standard deviation is 1.12 minutes.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Use the samples to find the mean completion time of the for the
1. male runners.
2. female runners.
Use the samples to find the sample standard deviation of the completion times for the
1. male runners.
2. female runners.
Find a point estimate for the mean completion time of the
1. male runners.
2. female runners.
Construct a 95% confidence interval for the population mean completion time of the
1. male runners.
2. female runners.
Interpret the results of number 4.
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.
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.
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 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
1. male runners. Assume the population standard deviation is 0.64 minutes.
2. female runners. Assume the population standard deviation is 1.12 minutes.

Country
Men's Name
Time in
Minutes
GBR
Mohamed FARAH
27.09
ETH
Tamirat TOLA
27.11
wwm
USA
Galen RUPP
27.15
Bedan Karoki MUCHIRI
Nguse AMLOSOM
Geoffrey
KEN
27.38
ww www
ERI
27.51
KEN
KAMWOROR
27.53
TUR
Polat Kembaoi ARIKAN
www
27.59
ETH
Abadi HADIS
27.61
JPN
Suguru OSAKO
27.87
USA
Shadrack KIPCHIRCHIR
27.97
PER
Luis OSTOS
28.03
UGA
28.08
Timothy TOROITICH
Andrew VERNON
Olivier IRABARUTA
GBR
28.32
BDI
28.55
JPN
Yuta SHITARA
28.92
GBR
Ross MILLINGTON
29.25
Country
Women's Name
Time in minutes
ETH
Almaz AYANA
www
29.29
ETH
Tirunesh DIBABA
ww
29.71
KEN
Betsy SAINA
30.13
TUR
Yasemin CAN
30.44
Karoline Bjerkell GROVDAL
www
NOR
31.24
USA
Emily INFELD
31.45
BDI
Diane NUKURI
31.48
GBR
Joanne PAVEY
31.56
GRE
Alexi PAPPAS
31.60
Darya MASLOVA
Dominique SCTT
Alia Saeed MOHAMMED
KGZ
31.62
RSA
31.86
UAE
31.95
CAN
Lanni MARCHANT
32.07
Salome NYIRARUKUNDO
Trihas GEBRE
Tatiele Roberta DE CARVALHO
RWA
32.13
ESP
32.16
BRA
32.64
USA
Marielle HALL
32.66
MEX
Marisol ROMERO
35.55
+

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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