Question

A running coach wants to know if participating in weekly running clubs significantly improves the time to run a mile. The running coach collects mean mile times for 42 runners who participate in weekly running clubs with 54 runners who do not run in clubs. The running coach measures times in January and June of the same year. All times are in seconds, and the runners all started with mile times between 8 minutes (480 seconds) and 9 minutes (540 seconds). Here are the results:

January June Change
Mean (seconds) StDev (seconds) Mean (seconds) StDev (seconds) Mean (seconds) StDev (seconds)
Running Club N = 42 530 28 520 23 10 4
Not in a Club N = 54 527 25 519 22 8 3
What is the best method for the running coach to use to determine if participating in weekly running clubs significantly improves the time to run a mile?
A) Use the difference in sample means (530 – 520) in a hypothesis test for a difference in two population means.
B) Use the difference in sample means (10 and 8) in a hypothesis test for a difference in two population means.
C) Use the sample mean 10 in a hypothesis test for a population mean.

Answer 1

Option B is correct.

Use the difference in sample means (10 and 8) in a hypothesis test for a difference in two population means.

Explanation:

The clear, complete table For this question is presented in the attached image to this solution.

It should be noted that For this question, the running coach wants to test if participating in weekly running clubs significantly improves the time to run a mile.

In the data setup, the mean time to run a mile in January for those that participate in weekly running clubs and those that do not was provided.

The mean time to run a mile in June too is provided for those that participate in weekly running clubs and those that do not.

Then the difference in the mean time to run a mile in January and June for the two classes (those that participate in weekly running clubs and those that do not) is also provided.

Since, the aim of the running coach is to test if participating in weekly running clubs significantly improves the time to run a mile, so, it is logical that it is the improvements in running times for the two groups that should be compared.

Hence, we should use the difference in sample means (10 and 8) in a hypothesis test for a difference in two population means.

Hope this Helps!!!