MATLAB: An Introduction with Applications
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
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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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