A test of abstract reasoning is given to a random sample of students before and after they complete a formal logic course. Test the claim that the mean score is not affected by the course. How many populations? 01 What is the parameter? Mean O Proportion O Variance Standard Deviation O Difference between Means

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A test of abstract reasoning is given to a random sample of students before and after they complete a formal logic course. Test the claim that the mean score is not affected by the course.

**How many populations?**

- ○ 2
- ○ 1

**What is the parameter?**

- ○ Mean
- ○ Proportion
- ○ Variance
- ○ Standard Deviation
- ○ Difference between Means
Transcribed Image Text:A test of abstract reasoning is given to a random sample of students before and after they complete a formal logic course. Test the claim that the mean score is not affected by the course. **How many populations?** - ○ 2 - ○ 1 **What is the parameter?** - ○ Mean - ○ Proportion - ○ Variance - ○ Standard Deviation - ○ Difference between Means
The image contains a series of statistical formulas for different test statistics. Each formula is presented with a selection option, indicated by a small circle. Here’s a detailed transcription and description of each formula:

### Title:
**What is the test statistic?**

1. **Chi-Square (\( \chi^2 \)):**
   \[
   \chi^2 = \frac{{(n - 1)^2 \cdot s^2}}{\sigma^2}
   \]

2. **Z-test for Proportions:**
   \[
   z = \frac{{\hat{p} - p}}{\sqrt{\frac{{p \cdot q}}{n}}}
   \]

3. **T-test for One Sample (\( t_d \)):**
   \[
   t_d = \frac{{\bar{x} - \mu_d}}{\frac{s_d}{\sqrt{n}}}
   \]

4. **Z-test for Two Proportions:**
   \[
   z = \frac{{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}}{\sqrt{\frac{{p \cdot q}}{n_1} + \frac{{p \cdot q}}{n_2}}}
   \]

5. **Z-test for Means:**
   \[
   z = \frac{{\bar{x} - \mu}}{\frac{\sigma}{\sqrt{n}}}
   \]

6. **Z-test for Two Means:**
   \[
   z = \frac{{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}
   \]

7. **T-test for Two Independent Samples (\( t \)):**
   \[
   t = \frac{{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}
   \]

8. **Z-test for Two Means with Proportions:**
   \[
   z = \frac{{(\bar{x}_1 - \bar{x}_2
Transcribed Image Text:The image contains a series of statistical formulas for different test statistics. Each formula is presented with a selection option, indicated by a small circle. Here’s a detailed transcription and description of each formula: ### Title: **What is the test statistic?** 1. **Chi-Square (\( \chi^2 \)):** \[ \chi^2 = \frac{{(n - 1)^2 \cdot s^2}}{\sigma^2} \] 2. **Z-test for Proportions:** \[ z = \frac{{\hat{p} - p}}{\sqrt{\frac{{p \cdot q}}{n}}} \] 3. **T-test for One Sample (\( t_d \)):** \[ t_d = \frac{{\bar{x} - \mu_d}}{\frac{s_d}{\sqrt{n}}} \] 4. **Z-test for Two Proportions:** \[ z = \frac{{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}}{\sqrt{\frac{{p \cdot q}}{n_1} + \frac{{p \cdot q}}{n_2}}} \] 5. **Z-test for Means:** \[ z = \frac{{\bar{x} - \mu}}{\frac{\sigma}{\sqrt{n}}} \] 6. **Z-test for Two Means:** \[ z = \frac{{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}} \] 7. **T-test for Two Independent Samples (\( t \)):** \[ t = \frac{{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \] 8. **Z-test for Two Means with Proportions:** \[ z = \frac{{(\bar{x}_1 - \bar{x}_2
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