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: (table) The running coach conducts a hypothesis test and finds that running club members significantly improve their running times with a p-value < 0.05. The running coach wants to calculate how many seconds change to expect for runners who participate in running clubs. What is the best method for the running coach to use to determine how many seconds change to expect for runners who participate in running clubs? Use the difference in sample means (530 − 520) in a hypothesis test for a difference in two population means (or treatment effect). Use the sample mean 10 to calculate a confidence interval for a population mean. Use the difference in sample means (530 − 520) to calculate a confidence interval for a difference in two population means (or treatment effect). Use the difference in sample means (10 and 8) in a hypothesis test for a difference in two population means (or treatment effect).
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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: (table)
The running coach conducts a hypothesis test and finds that running club members significantly improve their running times with a p-value < 0.05. The running coach wants to calculate how many seconds change to expect for runners who participate in running clubs.
What is the best method for the running coach to use to determine how many seconds change to expect for runners who participate in running clubs?
- Use the difference in sample means (530 − 520) in a hypothesis test for a difference in two population means (or treatment effect).
- Use the sample mean 10 to calculate a confidence interval for a population mean.
- Use the difference in sample means (530 − 520) to calculate a confidence interval for a difference in two population means (or treatment effect).
- Use the difference in sample means (10 and 8) in a hypothesis test for a difference in two population means (or treatment effect).
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