A marathon is a foot race with a distance of 26.22 miles. It was one of the original events of the modern Olympics, where it was a men's only event. The women's marathon became an Olympic event in 1984. 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. 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.

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.

Exercises:

1.Use the sample to find the point estimate for the mean training time of the

a.male runners.

b.female runners.

2.Find the sample standard deviation of the training times for the

a.male runners.

Training Time, x

Deviation,

Squares,

b.female runners.

Training Time, x

Deviation,

Squares,

3.Use the sample to construct a 95% confidence interval for the population mean training time of the

a.male runners.

b.female runners.

4.Interpret the results from Exercise 3.

a.

b.

5.Use the sample to construct a 95% confidence interval for the population mean training time of all runners. How do the 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 (Round to the nearest whole number.)

a.male runners. Assume the population standard deviation is 8.9 minutes.

b.female runners. Assume the population standard deviation is 8.4 minutes.