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 investigates if runners in a running club improve times more than runners not in a club. The running coach conducts a hypothesis test for the difference in sample mean change (“Running Club” minus “Not in a Club”). Here are the results: T-value = 2.7027, p-value = 0.0043, DF = 74 95% Confidence Interval (0.5254, 3.4746) Which of the following can the running coach c
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 investigates if runners in a running club improve times more than runners not in a club. The running coach conducts a hypothesis test for the difference in sample mean change (“Running Club” minus “Not in a Club”). Here are the results:
T-value = 2.7027, p-value = 0.0043, DF = 74
95% Confidence Interval (0.5254, 3.4746)
Which of the following can the running coach conclude?
- Runners who participate in running clubs have a statistically significant change in running times when compared to runners in not in a running club.
- The running coach is 95% confident that runners who participate in running clubs have changes in running times 0.5% to 3.5% higher than changes in the runners not in a running club.
- The alternative claim of statistically significant differences is valid. Runners who participate in running clubs have changes in running times 0.5% to 3.5% higher than changes in the runners not in a running club.
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