Mastery Check Solutions
Show What You Know
The track coaches at the Colossal Speed Camp tested a new warm-up method for 80 teen athletes running the 100-meter sprint.
| Group n = 40 |
Mean Sprint Time | Mean Pulse-Rate Recovery Time |
| Treatment: dynamic stretching | 13.8 sec | 4.2 min |
| Control: static stretching | 14.3 sec | 4.7 min |
| Observed difference | 0.5 sec | 0.5 min |
| Standard deviation | 0.21 sec | 0.38 min |
Simulation Results: A randomized test with 10,000 simulations was performed. The observed difference and standard deviation are reported in the table.
Additional Information:
- Dynamic stretching: stretching while moving
- Static stretching: stretching while holding
- Pulse-rate recovery: a measure of cardiovascular fitness, faster recovery means an athlete is more in shape and has a lower risk of injury
- In competitive races, 0.5 seconds can be the difference between first and last place.
- Coaches expect athletes to compete in races from November through June.
- Calculate both z-scores. Explain the statistical significance at the 5% level.
Dynamic stretching is statistically significant at the 5% level because the z-score is greater than 1.96. Pulse-rate recovery time is not statistically significant because the z-score is less than 1.96.
Note
Q: If a variable is not statistically significant, does that mean it is not important? Explain.
A: No, it could still be practically significant.
- Practically speaking, why do you think the track coaches also monitor pulse-rate recovery time?
Sample: Coaches monitor recovery time because they want to lower the risk of injury for athletes. If injuries are lower, the athletes can compete in more races.
- What type of stretching would you recommend the track coaches require for athletes during the season? Consider the statistical and practical implications for athletes.
Sample: Dynamic stretching improves immediate performance, meaning athletes are finishing races faster. It also improves recovery time, which is important for a long competition season.
Note
Q: Why would coaches want both performance measures? Explain.
A: Having both measures provides the coaches with a more complete picture of the athletes.
Say What You Know
In your own words, talk about what you have learned using the objectives for this lesson and your work on this page.
Note
Restate the objectives of the lesson in your own words. If you are unable to restate the lesson objectives, go back and reread the objectives and then explain them.
- Compare two treatments in an experiment to decide if the differences are significant.
- Analyze decisions using inferential statistics.