
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![## Hypothesis Testing for Pre-Test and Post-Test Scores
### Problem Statement
You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.01\). For the context of this problem, the first data set represents a pre-test and the second data set represents a post-test. You'll have to be careful about the direction in which you subtract.
- **Null Hypothesis (\(H_0\))**: \(\mu_d = 0\)
- **Alternative Hypothesis (\(H_a\))**: \(\mu_d > 0\)
### Background Information
You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for \(n = 46\) subjects. The average difference (post - pre) is \(\overline{d} = 6.2\) with a standard deviation of the differences of \(s_d = 35.3\).
### Questions to Answer
1. **Test Statistic Calculation**
- **What is the test statistic for this sample?**
Calculate and round to 4 decimal places.
\[
\text{test statistic} = \boxed{}
\]
2. **P-Value Determination**
- **What is the p-value for this sample?** Round to 4 decimal places.
\[
\text{p-value} = \boxed{}
\]
3. **P-Value Comparison**
- **The p-value is:**
- \(\mathbf{o}\) less than (or equal to) \(\alpha\)
- \(\mathbf{o}\) greater than \(\alpha\)
4. **Null Hypothesis Decision**
- **This test statistic leads to a decision to:**
- \(\mathbf{o}\) reject the null
- \(\mathbf{o}\) accept the null
- \(\mathbf{o}\) fail to reject the null
5. **Final Conclusion**
- **As such, the final conclusion is that...**
### Explanation of Terms and Calculations
- **Test Statistic**: This is a standardized value derived from sample data during a hypothesis test. It is calculated using the formula for t-test statistics based on sample means and standard deviations.
- **P-Value**: The probability that the observed results would occur if](https://content.bartleby.com/qna-images/question/a35d32dc-632b-40fd-aa41-e2c0040899b1/ac88888c-06fd-4298-9fc7-90bdcd150d58/g9qkr1r_thumbnail.png)
Transcribed Image Text:## Hypothesis Testing for Pre-Test and Post-Test Scores
### Problem Statement
You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.01\). For the context of this problem, the first data set represents a pre-test and the second data set represents a post-test. You'll have to be careful about the direction in which you subtract.
- **Null Hypothesis (\(H_0\))**: \(\mu_d = 0\)
- **Alternative Hypothesis (\(H_a\))**: \(\mu_d > 0\)
### Background Information
You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for \(n = 46\) subjects. The average difference (post - pre) is \(\overline{d} = 6.2\) with a standard deviation of the differences of \(s_d = 35.3\).
### Questions to Answer
1. **Test Statistic Calculation**
- **What is the test statistic for this sample?**
Calculate and round to 4 decimal places.
\[
\text{test statistic} = \boxed{}
\]
2. **P-Value Determination**
- **What is the p-value for this sample?** Round to 4 decimal places.
\[
\text{p-value} = \boxed{}
\]
3. **P-Value Comparison**
- **The p-value is:**
- \(\mathbf{o}\) less than (or equal to) \(\alpha\)
- \(\mathbf{o}\) greater than \(\alpha\)
4. **Null Hypothesis Decision**
- **This test statistic leads to a decision to:**
- \(\mathbf{o}\) reject the null
- \(\mathbf{o}\) accept the null
- \(\mathbf{o}\) fail to reject the null
5. **Final Conclusion**
- **As such, the final conclusion is that...**
### Explanation of Terms and Calculations
- **Test Statistic**: This is a standardized value derived from sample data during a hypothesis test. It is calculated using the formula for t-test statistics based on sample means and standard deviations.
- **P-Value**: The probability that the observed results would occur if
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