MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Rounding policy:
- Proportion: 4 decimal places
- Percentile: round to the closest whole unit number
- All others: 2 decimal places
Transcribed Image Text:### Problem 7
A population has \( \mu = 60 \) and \( \sigma = 10 \). Find the z-score corresponding to each of the following sample means:
a. A sample of \( n = 4 \) with \( M = 55 \)
b. A sample of \( n = 25 \) with \( M = 55 \)
c. A sample of \( n = 100 \) with \( M = 55 \)
d. What do we notice about the z-scores as the sample size changes?
### Problem 8
If you are taking a random sample from a normal population with \( \mu = 100 \) and \( \sigma = 16 \), which of the following outcomes is more likely? Explain your answer.
a. A sample mean greater than 106 for a sample of \( n = 4 \).
b. A sample mean greater than 103 for a sample of \( n = 36 \).
![**Study on the Effectiveness of Relaxation Training in Reducing Anxiety**
A researcher evaluated the effectiveness of relaxation training in reducing anxiety. One sample of anxiety-ridden people received relaxation training, while a second sample did not. Then anxiety scores were measured for all subjects using a standardized test. Use the information summarized in the following table to complete this item.
**Table: The Effect of Relaxation Training on Anxiety Scores**
| Group | Mean Anxiety Score | SE (Standard Error) |
|---------------------|--------------------|---------------------|
| Control group | 36 | 7 |
| Relaxation training | 18 | 5 |
**Questions:**
a. **What is the independent variable (IV)?**
- The independent variable is the type of group (Control group vs. Relaxation training).
b. **How many levels do we have for the IV?**
- There are two levels for the independent variable: Control group and Relaxation training.
c. **What is the level of measurement for the IV?**
- The level of measurement for the IV is nominal (categorical).
d. **What is the DV (dependent variable, remember, the DV is the data)?**
- The dependent variable is the Mean Anxiety Score.
e. **What is the level of measurement of the DV?**
- The level of measurement for the DV is interval.
f. **What is the best graph to display this data? Explain.**
- A bar graph would be the best way to display this data as it allows comparison of mean anxiety scores between two categorical groups with their respective standard errors.
g. **Construct a graph (by hand) that incorporates all the information in this table.**
- [Instructions for creating a bar graph: Draw two bars, one for each group. Label the y-axis with mean anxiety scores ranging from 0 to 40. Place the control group at a mean score of 36 with an error bar extending from 29 to 43. Place the relaxation training group at a mean score of 18 with an error bar extending from 13 to 23.]
h. **Looking at your graph, do you think that the relaxation training really worked? Explain your answer.**
- Based on the graph, relaxation training appears to be effective in reducing anxiety as the mean anxiety score for the relaxation training group is substantially lower than for the](https://content.bartleby.com/qna-images/question/e39e6f31-fb38-4df4-8e11-f23a384cb477/65b7ca00-4f5a-40bd-9c18-c053a7cc65db/zxox7ic_processed.png)
Transcribed Image Text:**Study on the Effectiveness of Relaxation Training in Reducing Anxiety**
A researcher evaluated the effectiveness of relaxation training in reducing anxiety. One sample of anxiety-ridden people received relaxation training, while a second sample did not. Then anxiety scores were measured for all subjects using a standardized test. Use the information summarized in the following table to complete this item.
**Table: The Effect of Relaxation Training on Anxiety Scores**
| Group | Mean Anxiety Score | SE (Standard Error) |
|---------------------|--------------------|---------------------|
| Control group | 36 | 7 |
| Relaxation training | 18 | 5 |
**Questions:**
a. **What is the independent variable (IV)?**
- The independent variable is the type of group (Control group vs. Relaxation training).
b. **How many levels do we have for the IV?**
- There are two levels for the independent variable: Control group and Relaxation training.
c. **What is the level of measurement for the IV?**
- The level of measurement for the IV is nominal (categorical).
d. **What is the DV (dependent variable, remember, the DV is the data)?**
- The dependent variable is the Mean Anxiety Score.
e. **What is the level of measurement of the DV?**
- The level of measurement for the DV is interval.
f. **What is the best graph to display this data? Explain.**
- A bar graph would be the best way to display this data as it allows comparison of mean anxiety scores between two categorical groups with their respective standard errors.
g. **Construct a graph (by hand) that incorporates all the information in this table.**
- [Instructions for creating a bar graph: Draw two bars, one for each group. Label the y-axis with mean anxiety scores ranging from 0 to 40. Place the control group at a mean score of 36 with an error bar extending from 29 to 43. Place the relaxation training group at a mean score of 18 with an error bar extending from 13 to 23.]
h. **Looking at your graph, do you think that the relaxation training really worked? Explain your answer.**
- Based on the graph, relaxation training appears to be effective in reducing anxiety as the mean anxiety score for the relaxation training group is substantially lower than for the
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