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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Section10.6: Summarizing Categorical Data
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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).**
Transcribed Image Text:### 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).**
### 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
Transcribed Image Text:### 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
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