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
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
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 24HP
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9076e7a-57c1-402a-997f-53718f1a9a67%2Ff2ba253d-0f1b-43ac-8261-f64fae176e70%2Fqvljpgn_processed.png&w=3840&q=75)
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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