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).
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa35d32dc-632b-40fd-aa41-e2c0040899b1%2Fa5df425d-d3d6-4f75-9991-771098c1b6b9%2F3veqwte_processed.png&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 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa35d32dc-632b-40fd-aa41-e2c0040899b1%2Fa5df425d-d3d6-4f75-9991-771098c1b6b9%2Fd2f0afe_processed.png&w=3840&q=75)
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