MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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
expand button
Transcribed Image Text: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.
expand button
Transcribed Image Text: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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