A study on facial expression and anxiety was conducted to determine if anxious people exhibit more facial expressions than non-anxious people. The number of facial expressions exhibited in response to 25 emotional cues for 25 anxious subjects and 25 non-anxious subjects are shown below (each group includes a different set of 25 people).
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A study on facial expressions and anxiety was conducted to determine if anxious people exhibit more facial expressions than non-anxious people. The number facial expressions exhibited in response to 25 emotional cues for 25 anxious subjects and 25 non anxious subjects are shown below (each group includes a different set of 25 people)
![### Statistical Testing of Anxious and Non-Anxious Groups
**Hypothesis Testing**
Given the following hypotheses and a significance level of \(\alpha = 0.05\):
- Null Hypothesis (\(H_0\)): \(\mu_2 - \mu_1 = 0\)
- Alternative Hypothesis (\(H_a\)): \(\mu_2 - \mu_1 < 0\)
Where group 2 represents the non-anxious group and group 1 represents the anxious group.
**Tasks**
a) **Calculate the test statistic.**
b) **Find the p-value.**
c) **State the conclusion (in the context of the problem).**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27b4802f-f0fe-408d-90d1-a8d89e62e50b%2Ffd850a48-f566-491f-8bd4-cfd51cdc36bf%2Fddfvd1s.jpeg&w=3840&q=75)
![### Study on Facial Expressions and Anxiety
A study on facial expression and anxiety was conducted to determine if anxious people exhibit more facial expressions than non-anxious people. The number of facial expressions exhibited in response to 25 emotional cues for 25 anxious subjects and 25 non-anxious subjects are shown below (each group includes a different set of 25 people).
#### Data Table: Number of Facial Expressions
| **Anxious** | **Non-Anxious** |
|-------------|-----------------|
| 2 | 4 |
| 12 | 17 |
| 17 | 12 |
| 15 | 13 |
| 27 | 15 |
| 18 | 8 |
| 28 | 15 |
| 16 | 16 |
| 16 | 13 |
| 19 | 12 |
| 11 | 10 |
| 25 | 18 |
| 13 | 14 |
| 11 | 9 |
| 23 | 9 |
| 5 | 18 |
| 3 | 16 |
| 26 | 15 |
| 11 | 18 |
| 16 | 14 |
| 26 | 14 |
| 18 | 15 |
| 26 | 9 |
| 20 | 17 |
| 19 | 17 |
This dataset can help in understanding whether there is a significant difference in the number of facial expressions exhibited by anxious subjects compared to non-anxious subjects in response to emotional cues. For further analysis, you may consider statistical measures such as mean, median, standard deviation, and conducting hypothesis tests.
### Graphical Representation
For better visualization, it is recommended to use the following types of graphs:
1. **Box Plot**: A box plot for each group (Anxious vs. Non-Anxious) can illustrate the distribution, median, and interquartile range of the data.
2. **Histogram**: Individual histograms can show the frequency distribution of the number of facial expressions for each group.
3. **Scatter Plot**: A scatter plot may help in visualizing any correlation between the number of facial expressions and the anxiety level.
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27b4802f-f0fe-408d-90d1-a8d89e62e50b%2Ffd850a48-f566-491f-8bd4-cfd51cdc36bf%2Fb5o6lc.jpeg&w=3840&q=75)
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