Help!! ### Hypothesis TestingUsing the hypothesis below 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 is the non-anxious group and group 1 is the anxious group.#### Steps:##### a) Calculate the Test Statistic**Instruction**: Compute the test statistic based on the sample data provided from the two groups. Generally, the test statistic for comparing two means can be calculated as:\[t = \frac{(\bar{X}_2 - \bar{X}_1) - 0}{\sqrt{s_1^2/n_1 + s_2^2/n_2}}\]Where:- $\bar{X}_2$ and $\bar{X}_1$ are the sample means of group 2 and group 1, respectively.- $s_2$ and $s_1$ are the sample standard deviations of group 2 and group 1, respectively.- $n_2$ and $n_1$ are the sample sizes of group 2 and group 1, respectively.**Note**: Use the data provided to compute these values if given.##### b) Find the p-value**Instruction**: Determine the p-value associated with the test statistic. This involves looking up the value in a t-distribution table or using software that calculates it based on the degrees of freedom.##### c) State the Conclusion (in the context of the problem)**Instruction**: Based on the calculated p-value, state whether you reject or fail to reject the null hypothesis at the $ \alpha = 0.05 $ significance level. Conclude what this decision means in the context of the anxiety levels of the two groups.**Example Conclusion**: - If $ p \leq \alpha $: Reject $ H_0 $. There is sufficient evidence to conclude that the mean of the non-anxious group is significantly lower than the mean of the anxious group.- If $ p > \alpha $: Fail to reject $ H_0 $. There is not sufficient evidence to conclude that there is a difference ### Study on Facial Expressions and AnxietyA 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 in the table below (each group includes a different set of 25 people).| 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 |#### Explanation of Data- **Columns:** Each column represents a different group of subjects. - The **Anxious** column lists the number of facial expressions made by each of the 25 anxious subjects. - The **Non-Anxious** column lists the number of facial expressions made by each of the 25 non-anxious subjects.This data can be used to compare the average number of facial expressions exhibited by anxious versus non-anxious individuals, potentially revealing insights into how anxiety affects expressive behavior.

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Description: Help!! ### Hypothesis TestingUsing the hypothesis below 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 is the non-an

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Using the hypothesis below and a significance level of =0.05 , Ho: µ2 – H1 = 0 Ha: l2 – H1 < 0 Where group 2 is the non-anxious group and group 1 is the anxious group a) Calculate the test statistic b) Find the p-value c) State the conclusion (in the context of the problem).

Using the hypothesis below and a significance level of =0.05 , Ho: µ2 – H1 = 0 Ha: l2 – H1 < 0 Where group 2 is the non-anxious group and group 1 is the anxious group a) Calculate the test statistic b) Find the p-value c) State the conclusion (in the context of the problem).

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Help!!

### Hypothesis Testing

Using the hypothesis below 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 is the non-anxious group and group 1 is the anxious group.

#### Steps:

##### a) Calculate the Test Statistic

**Instruction**: Compute the test statistic based on the sample data provided from the two groups. Generally, the test statistic for comparing two means can be calculated as:

\[
t = \frac{(\bar{X}_2 - \bar{X}_1) - 0}{\sqrt{s_1^2/n_1 + s_2^2/n_2}}
\]

Where:
- $\bar{X}_2$ and $\bar{X}_1$ are the sample means of group 2 and group 1, respectively.
- $s_2$ and $s_1$ are the sample standard deviations of group 2 and group 1, respectively.
- $n_2$ and $n_1$ are the sample sizes of group 2 and group 1, respectively.

**Note**: Use the data provided to compute these values if given.

##### b) Find the p-value

**Instruction**: Determine the p-value associated with the test statistic. This involves looking up the value in a t-distribution table or using software that calculates it based on the degrees of freedom.

##### c) State the Conclusion (in the context of the problem)

**Instruction**: Based on the calculated p-value, state whether you reject or fail to reject the null hypothesis at the $ \alpha = 0.05 $ significance level. Conclude what this decision means in the context of the anxiety levels of the two groups.

**Example Conclusion**:

- If $ p \leq \alpha $: Reject $ H_0 $. There is sufficient evidence to conclude that the mean of the non-anxious group is significantly lower than the mean of the anxious group.
- If $ p > \alpha $: Fail to reject $ H_0 $. There is not sufficient evidence to conclude that there is a difference

### 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 in the table below (each group includes a different set of 25 people).

| 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 |

#### Explanation of Data

- **Columns:** Each column represents a different group of subjects.
- The **Anxious** column lists the number of facial expressions made by each of the 25 anxious subjects.
- The **Non-Anxious** column lists the number of facial expressions made by each of the 25 non-anxious subjects.

This data can be used to compare the average number of facial expressions exhibited by anxious versus non-anxious individuals, potentially revealing insights into how anxiety affects expressive behavior.

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