What is the test statistic? (#1 – #2) – (41 – µ2) OF Ot ta (T1 – ã2) – (41 – µ2) (P1 – P2) – (P1 – p2) Ot = (n – 1)² . s² +

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The image presents a series of equations used to determine different statistical test statistics. Here's a transcription and description for educational purposes:

**What is the test statistic?**

1. \( \bigcirc \, F = \frac{s_1^2}{s_2^2} \)

2. \( \bigcirc \, t_d = \frac{\bar{x} - \mu_d}{s_d / \sqrt{n}} \)

3. \( \bigcirc \, z = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}} \)

4. \( \bigcirc \, t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \)

5. \( \bigcirc \, z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}} \)

6. \( \bigcirc \, t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \)

7. \( \bigcirc \, t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{\hat{p} \cdot \hat{q}}{n_1} + \frac{\hat{p} \cdot \hat{q}}{n_2}}} \)

8. \( \bigcirc \, z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \)

9. \( \bigcirc \, z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\frac{\hat{p} \cdot \hat{q}}{n_1} + \frac{\hat{p} \cdot \hat{q}}{n_2}}} \)

10. \( \bigcirc \, \chi^2 = \frac{
Transcribed Image Text:The image presents a series of equations used to determine different statistical test statistics. Here's a transcription and description for educational purposes: **What is the test statistic?** 1. \( \bigcirc \, F = \frac{s_1^2}{s_2^2} \) 2. \( \bigcirc \, t_d = \frac{\bar{x} - \mu_d}{s_d / \sqrt{n}} \) 3. \( \bigcirc \, z = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}} \) 4. \( \bigcirc \, t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \) 5. \( \bigcirc \, z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}} \) 6. \( \bigcirc \, t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \) 7. \( \bigcirc \, t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{\hat{p} \cdot \hat{q}}{n_1} + \frac{\hat{p} \cdot \hat{q}}{n_2}}} \) 8. \( \bigcirc \, z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \) 9. \( \bigcirc \, z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\frac{\hat{p} \cdot \hat{q}}{n_1} + \frac{\hat{p} \cdot \hat{q}}{n_2}}} \) 10. \( \bigcirc \, \chi^2 = \frac{
**Research Study on Helping Behavior**

A study examines the behavior of two groups regarding their likelihood to help others in need:

- **Group 1:** Out of 1000 individuals who attend religious services at least once a week, 31 stopped to help a person with car trouble.
  
- **Group 2:** Out of 1200 individuals who do not attend religious services at least once a month, 22 stopped to help a person with car trouble.

The objective is to test the claim that the proportion of people who help in each group is equal.

**Questions and Concepts:**

1. **How many populations are being compared?**
   - Options:
     - \( \circ \) 2
     - \( \circ \) 1

2. **What is the parameter being tested?**
   - Options:
     - \( \circ \) Variance
     - \( \circ \) Proportion
     - \( \circ \) Mean
     - \( \circ \) Difference between Means
     - \( \circ \) Standard Deviation

Understanding these questions and the analysis involved will help in evaluating the differences or similarities in behaviors between these distinct groups.
Transcribed Image Text:**Research Study on Helping Behavior** A study examines the behavior of two groups regarding their likelihood to help others in need: - **Group 1:** Out of 1000 individuals who attend religious services at least once a week, 31 stopped to help a person with car trouble. - **Group 2:** Out of 1200 individuals who do not attend religious services at least once a month, 22 stopped to help a person with car trouble. The objective is to test the claim that the proportion of people who help in each group is equal. **Questions and Concepts:** 1. **How many populations are being compared?** - Options: - \( \circ \) 2 - \( \circ \) 1 2. **What is the parameter being tested?** - Options: - \( \circ \) Variance - \( \circ \) Proportion - \( \circ \) Mean - \( \circ \) Difference between Means - \( \circ \) Standard Deviation Understanding these questions and the analysis involved will help in evaluating the differences or similarities in behaviors between these distinct groups.
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