3:19 1Data Project #4: ConfidenceIntervalsA marathon is a foot race with a distanceof 26.22 miles. The Olympic record forthe women's marathon was set during the2012 Olympics by Tiki Gelana of Ethiopia,with a time of 2 hours, 23 minutes, 7seconds. The Olympic record for themen's marathon was set during the 2008Olympics by Samuel Kamau Wanjiru ofKenya, with a time of 2 hours, 6 minutes,32 seconds.Training for a marathon typically lasts atleast 6 months. The training is gradual,with increases in distance about every 2weeks. About 1 to 3 weeks before the race,the distance run is decreased slightly. Thestem-and-leaf plots below show themarathon training times (in minutes) for arandom sample of 30 male runners and30 female runners.Training Times (in minutes)of Female Runners17 | 8 9 918 0 0 0 0 1 2 319 0 0 0 1 3 4 5 56620 0 01 2 3Key: 17|8 = 1786 6 7 9Training Times (in minutes)of Male Runners15 5 89 9916 0 0 0 01 2 3 4 45 8 917 0 1 1 356 6 7 7 918 015Key: 15|5 - 1551. Use the sample to find a pointestimate for the mean training timeof thea. female runnersb. male runners.2. Find the sample standarddeviation of the training times fortheo. female runners 3:19 120 0 01 2 3Training Times (in minutes)of Male Runners15 | 5 8 9 9 9 Key: 15|5 = 15516 0 0 0 0 1 2 3 4 4 5 8 917 0 1 1 3 5 6 6 7 7918 0 151. Use the sample to find a pointestimate for the mean training timeof thea. female runnersb. male runners.2. Find the sample standarddeviation of the training times forthea. female runnersb. male runners3. Use the sample to construct a 95%confidence interval for thepopulation mean training time ofthea. female runnersb. male runners4. Illustrate and interpret the resultsof # 3.5. Use the sample to construct a 95%confidence interval for thepopulation mean training time ofall runners. How do your resultsdiffer from those in Exercise 3?Explain.6. A trainer wants to estimate thepopulation mean running times forboth male and female runnerswithin 2 minutes. Determine theminimum sample size required toconstruct a 99% confidence intervalfor the population mean trainingtime ofa. female runners. Assume thepopulation stondorddeviation is 8.4 minutesb. male runners. Assume thepopulation standarddeviation is 8.9 minutes.

Given information: Female 178, 179, 179, 180, 180, 180, 180, 181, 182, 183, 184, 186, 186, 187, 189,…

A marathon is a foot race with a distance of 26.22 miles. The Olympic record for the women's marathon wos set during the 2012 Olympics by Tiki Gelana of Ethiopia, with a time of 2 hours, 23 minutes, 7 seconds. The Olympic record for the men's marathon was set during the 2008 Olympics by Samuel Kamau Wanjiru of Kenyo, with a time of 2 hours, 6 minutes, 32 seconds. Training for a marathon typically lasts at least 6 months. The training is gradual, with increases in distance about every 2 weeks. About 1 to 3 weeks before the race, the distance run is decreased slightly. The stem-and-leaf plots below show the marathon training times (in minutes) for a random sample of 30 male runners and 30 female runners. Training Times (in minutes) of Female Runners 17 |8 9 9 18 0 0 0 0 1 23 46 6 7 9 19 0 0 013 45 56 6 20 | 0 01 2 3 Key: 17|8 - 178 Training Times (in minutes) of Male Runners 15 |5 8 9 9 9 Key: 15|5 - 155 16 0 0 0 0 1 2 3 4 4 5 8 9 17 01135 6 6 7 79 18 015 1. Use the sample to find a point estimate for the mean training time of the o. female runners 6. male runners. 2. Find the sample standard deviation of the training times for the

A marathon is a foot race with a distance of 26.22 miles. The Olympic record for the women's marathon wos set during the 2012 Olympics by Tiki Gelana of Ethiopia, with a time of 2 hours, 23 minutes, 7 seconds. The Olympic record for the men's marathon was set during the 2008 Olympics by Samuel Kamau Wanjiru of Kenyo, with a time of 2 hours, 6 minutes, 32 seconds. Training for a marathon typically lasts at least 6 months. The training is gradual, with increases in distance about every 2 weeks. About 1 to 3 weeks before the race, the distance run is decreased slightly. The stem-and-leaf plots below show the marathon training times (in minutes) for a random sample of 30 male runners and 30 female runners. Training Times (in minutes) of Female Runners 17 |8 9 9 18 0 0 0 0 1 23 46 6 7 9 19 0 0 013 45 56 6 20 | 0 01 2 3 Key: 17|8 - 178 Training Times (in minutes) of Male Runners 15 |5 8 9 9 9 Key: 15|5 - 155 16 0 0 0 0 1 2 3 4 4 5 8 9 17 01135 6 6 7 79 18 015 1. Use the sample to find a point estimate for the mean training time of the o. female runners 6. male runners. 2. Find the sample standard deviation of the training times for the

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

3:19 1
Data Project #4: Confidence
Intervals
A marathon is a foot race with a distance
of 26.22 miles. The Olympic record for
the women's marathon was set during the
2012 Olympics by Tiki Gelana of Ethiopia,
with a time of 2 hours, 23 minutes, 7
seconds. The Olympic record for the
men's marathon was set during the 2008
Olympics by Samuel Kamau Wanjiru of
Kenya, with a time of 2 hours, 6 minutes,
32 seconds.
Training for a marathon typically lasts at
least 6 months. The training is gradual,
with increases in distance about every 2
weeks. About 1 to 3 weeks before the race,
the distance run is decreased slightly. The
stem-and-leaf plots below show the
marathon training times (in minutes) for a
random sample of 30 male runners and
30 female runners.
Training Times (in minutes)
of Female Runners
17 | 8 9 9
18 0 0 0 0 1 2 3
19 0 0 0 1 3 4 5 566
20 0 01 2 3
Key: 17|8 = 178
6 6 7 9
Training Times (in minutes)
of Male Runners
15 5 89 99
16 0 0 0 01 2 3 4 45 8 9
17 0 1 1 356 6 7 7 9
18 015
Key: 15|5 - 155
1. Use the sample to find a point
estimate for the mean training time
of the
a. female runners
b. male runners.
2. Find the sample standard
deviation of the training times for
the
o. female runners

3:19 1
20 0 01 2 3
Training Times (in minutes)
of Male Runners
15 | 5 8 9 9 9 Key: 15|5 = 155
16 0 0 0 0 1 2 3 4 4 5 8 9
17 0 1 1 3 5 6 6 7 79
18 0 15
1. Use the sample to find a point
estimate for the mean training time
of the
a. female runners
b. male runners.
2. Find the sample standard
deviation of the training times for
the
a. female runners
b. male runners
3. Use the sample to construct a 95%
confidence interval for the
population mean training time of
the
a. female runners
b. male runners
4. Illustrate and interpret the results
of # 3.
5. Use the sample to construct a 95%
confidence interval for the
population mean training time of
all runners. How do your results
differ from those in Exercise 3?
Explain.
6. A trainer wants to estimate the
population mean running times for
both male and female runners
within 2 minutes. Determine the
minimum sample size required to
construct a 99% confidence interval
for the population mean training
time of
a. female runners. Assume the
population stondord
deviation is 8.4 minutes
b. male runners. Assume the
population standard
deviation is 8.9 minutes.

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