MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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#20 part b only- show full work for psych stats
Transcribed Image Text:### Exercise and Psychological Well-being
Exercise is known to produce positive psychological effects. Interestingly, not all exercise is equally effective. Research indicates that exercising in a natural environment (e.g., jogging in the woods) produces better psychological outcomes than exercising in urban environments or in homes (Mackay & Neill, 2010).
A sports psychologist is interested in testing whether there is a difference between exercise in nature and exercise in the lab concerning post-exercise anxiety levels. The researcher recruits \( n = 7 \) participants who exercise in the lab and on a nature trail. The following data represent the anxiety scores measured after each exercise session.
Transcribed Image Text:### Table of Anxiety Scores for Participants
| Participant | Anxiety after Exercising in Lab | Anxiety after Exercising in Nature |
|-------------|---------------------------------|----------------------------------|
| A | 32 | 8 |
| B | 66 | 68 |
| C | 52 | 48 |
| D | 48 | 37 |
| E | 52 | 44 |
| F | 48 | 38 |
| G | 52 | 44 |
### Statistical Questions
a. **Independent-Measures Study Analysis**
Treat the data as if the scores are from an independent-measures study using two separate samples, each with \( n = 7 \) participants. Compute the pooled variance, the estimated standard error for the mean difference, and the independent-measures t statistic. Using \( \alpha = .05 \), is there a significant difference between the two sets of scores?
b. **Repeated-Measures Study Analysis**
Assume the data are from a repeated-measures study using the same sample of \( n = 7 \) participants in both treatment conditions. Compute the variance for the sample of difference scores, the estimated standard error for the mean difference, and the repeated-measures t statistic. Using \( \alpha = .05 \), is there a significant difference between the two sets of scores?
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