MATLAB: An Introduction with Applications
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![**Hypothesis Testing Educational Exercise**
This example will guide you through testing a hypothesis at a significance level of \(\alpha = 0.005\), where one dataset represents pre-test scores and the other represents post-test scores.
### Hypotheses:
- **Null Hypothesis (\(H_0\))**: \(\mu_d = 0\)
- **Alternative Hypothesis (\(H_a\))**: \(\mu_d \ne 0\)
### Given Data:
You believe that the population of difference scores is normally distributed, but the standard deviation is unknown. You obtain pre-test and post-test samples for \( n = 172 \) subjects. The average difference (post - pre) is:
- Mean difference, \(\bar{d} = -2.3\)
- Standard deviation of the differences, \(s_d = 50.6\)
### Questions:
1. **What is the test statistic for this sample?**
- **Answer:**
\[
\text{test statistic} = \boxed{\hspace{50pt}}
\]
(Round to 4 decimal places.)
2. **What is the p-value for this sample?**
- **Answer:**
\[
\text{p-value} = \boxed{\hspace{50pt}}
\]
(Round to 4 decimal places.)
3. **The p-value is:**
- \(\circ\) less than (or equal to) \(\alpha\)
- \(\circ\) greater than \(\alpha\)
4. **This test statistic leads to a decision to:**
- \(\circ\) reject the null
- \(\circ\) accept the null
- \(\circ\) fail to reject the null
5. **As such, the final conclusion is that...**
- (Provide your conclusion based on the test results.)
This exercise provides practice with the calculation and interpretation of a hypothesis test, crucial for understanding inferential statistics.](https://content.bartleby.com/qna-images/question/a35d32dc-632b-40fd-aa41-e2c0040899b1/bb6fdad8-37c0-496b-af11-c79cf8245ea2/4axmvek_processed.png)
Transcribed Image Text:**Hypothesis Testing Educational Exercise**
This example will guide you through testing a hypothesis at a significance level of \(\alpha = 0.005\), where one dataset represents pre-test scores and the other represents post-test scores.
### Hypotheses:
- **Null Hypothesis (\(H_0\))**: \(\mu_d = 0\)
- **Alternative Hypothesis (\(H_a\))**: \(\mu_d \ne 0\)
### Given Data:
You believe that the population of difference scores is normally distributed, but the standard deviation is unknown. You obtain pre-test and post-test samples for \( n = 172 \) subjects. The average difference (post - pre) is:
- Mean difference, \(\bar{d} = -2.3\)
- Standard deviation of the differences, \(s_d = 50.6\)
### Questions:
1. **What is the test statistic for this sample?**
- **Answer:**
\[
\text{test statistic} = \boxed{\hspace{50pt}}
\]
(Round to 4 decimal places.)
2. **What is the p-value for this sample?**
- **Answer:**
\[
\text{p-value} = \boxed{\hspace{50pt}}
\]
(Round to 4 decimal places.)
3. **The p-value is:**
- \(\circ\) less than (or equal to) \(\alpha\)
- \(\circ\) greater than \(\alpha\)
4. **This test statistic leads to a decision to:**
- \(\circ\) reject the null
- \(\circ\) accept the null
- \(\circ\) fail to reject the null
5. **As such, the final conclusion is that...**
- (Provide your conclusion based on the test results.)
This exercise provides practice with the calculation and interpretation of a hypothesis test, crucial for understanding inferential statistics.
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