Migraine Acupun A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlle study where 167 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 69 patients in the treatment group received acupuncture that is
Migraine Acupun A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlle study where 167 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 69 patients in the treatment group received acupuncture that is
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Migraine and Acupuncture**
A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 167 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control.
- **Treatment Group**: 69 patients received acupuncture that is specifically designed to treat migraines.
- **Control Group**: 98 patients received placebo acupuncture (needle insertion at non-acupoint locations).
24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. Test to see if migraine pain relief is dependent on receiving acupuncture. Use α = 0.01.
### Contingency Table
| | Pain Free: Yes | Pain Free: No | Total |
|-------------------|----------------|---------------|-------|
| **Treatment** | 16 | 53 | 69 |
| **Control** | 7 | 91 | 98 |
| **Total** | 23 | 144 | 167 |
### Questions
a) **What is the correct null hypothesis?**
- \( \text{H}_0 \): Migraine pain relief is independent of receiving acupuncture.
- \( \text{H}_0 \): \( p_1 \neq p_2 \neq p_3 \neq p_4 \)
- \( \text{H}_0 \): Migraine pain relief is dependent on receiving acupuncture.
- \( \text{H}_0 \): \( p_1 = p_2 = p_3 = p_4 \)
b) **Fill in the expected values, round answers to at least 2 decimal places.**
### Expected Values Table
| | Pain Free: Yes | Pain Free: No |
|-------------------------|----------------|---------------|
| **Treatment** | | |
| **Control** | | |
To calculate the expected values for each cell, use the formula:
\[ E = \frac{(\text{row total} \times \text{column total})}{\text{grand total}} \]
For example, the expected value for the "Treatment" and "Pain Free: Yes" cell is:
\[ E = \frac{(69 \times 23)}{167} = 9.50 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e9d300d-1c07-4ae7-bdcf-7bcca0d57eba%2F25dccd34-f00c-48f9-9f12-6136f50fd8d6%2Fvgzrfwg.png&w=3840&q=75)
Transcribed Image Text:**Migraine and Acupuncture**
A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 167 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control.
- **Treatment Group**: 69 patients received acupuncture that is specifically designed to treat migraines.
- **Control Group**: 98 patients received placebo acupuncture (needle insertion at non-acupoint locations).
24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. Test to see if migraine pain relief is dependent on receiving acupuncture. Use α = 0.01.
### Contingency Table
| | Pain Free: Yes | Pain Free: No | Total |
|-------------------|----------------|---------------|-------|
| **Treatment** | 16 | 53 | 69 |
| **Control** | 7 | 91 | 98 |
| **Total** | 23 | 144 | 167 |
### Questions
a) **What is the correct null hypothesis?**
- \( \text{H}_0 \): Migraine pain relief is independent of receiving acupuncture.
- \( \text{H}_0 \): \( p_1 \neq p_2 \neq p_3 \neq p_4 \)
- \( \text{H}_0 \): Migraine pain relief is dependent on receiving acupuncture.
- \( \text{H}_0 \): \( p_1 = p_2 = p_3 = p_4 \)
b) **Fill in the expected values, round answers to at least 2 decimal places.**
### Expected Values Table
| | Pain Free: Yes | Pain Free: No |
|-------------------------|----------------|---------------|
| **Treatment** | | |
| **Control** | | |
To calculate the expected values for each cell, use the formula:
\[ E = \frac{(\text{row total} \times \text{column total})}{\text{grand total}} \]
For example, the expected value for the "Treatment" and "Pain Free: Yes" cell is:
\[ E = \frac{(69 \times 23)}{167} = 9.50 \]
![### Expected Values Table for Pain Relief Study
#### Instructions:
1. **b) Fill in the expected values**, round answers to at least 2 decimal places.
| **Expected Values** | **Pain Free: Yes** | **Pain Free: No** |
|---------------------|-------------------|------------------|
| **Treatment** | | |
| **Control** | | |
2. **Answers show on last attempt**
| | **Pain Free: Yes** | **Pain Free: No** |
|---------------------|-------------------|------------------|
| **Treatment** | | |
| **Control** | | |
3. **c) Find the test statistic**, round answer to at least 3 decimal places.
**Test Statistic:** [ ]
4. **d) What is the p-value?** Round answer to at least 3 decimal places.
**p-value:** [ ]
5. **e) What is the correct conclusion?**
- [ ] There is no statistical evidence that migraine pain relief is dependent on receiving acupuncture.
- [ ] There is statistical evidence that migraine pain relief is dependent on receiving acupuncture.
### Detailed Explanation:
- The table in part **(b)** is split into two columns under the header "Expected Values". One column is for "Pain Free: Yes" and the other is for "Pain Free: No". For each condition (Treatment or Control), you need to fill in the expected number of cases that fall into these categories.
- The table labeled **"Answers show on last attempt"** is formatted in the same way as the Expected Values table but is meant to reflect observed results from an experiment.
- In part **(c)**, you are required to **find the test statistic** for the data, which often involves calculating a Chi-square or another relevant statistical measure.
- For part **(d)**, you must determine the **p-value**, which indicates the probability that the observed results are due to chance.
- Finally, part **(e)** asks you to **draw a conclusion** from the test. You need to select whether there is or isn't statistical evidence that migraine pain relief is dependent on receiving acupuncture.
### Additional Notes:
Carefully calculate and cross-verify your expected values and observe the counts before proceeding to calculate the test statistic and p-value. Proper rounding to specified decimal places is crucial for an](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e9d300d-1c07-4ae7-bdcf-7bcca0d57eba%2F25dccd34-f00c-48f9-9f12-6136f50fd8d6%2F0fz5dd_processed.png&w=3840&q=75)
Transcribed Image Text:### Expected Values Table for Pain Relief Study
#### Instructions:
1. **b) Fill in the expected values**, round answers to at least 2 decimal places.
| **Expected Values** | **Pain Free: Yes** | **Pain Free: No** |
|---------------------|-------------------|------------------|
| **Treatment** | | |
| **Control** | | |
2. **Answers show on last attempt**
| | **Pain Free: Yes** | **Pain Free: No** |
|---------------------|-------------------|------------------|
| **Treatment** | | |
| **Control** | | |
3. **c) Find the test statistic**, round answer to at least 3 decimal places.
**Test Statistic:** [ ]
4. **d) What is the p-value?** Round answer to at least 3 decimal places.
**p-value:** [ ]
5. **e) What is the correct conclusion?**
- [ ] There is no statistical evidence that migraine pain relief is dependent on receiving acupuncture.
- [ ] There is statistical evidence that migraine pain relief is dependent on receiving acupuncture.
### Detailed Explanation:
- The table in part **(b)** is split into two columns under the header "Expected Values". One column is for "Pain Free: Yes" and the other is for "Pain Free: No". For each condition (Treatment or Control), you need to fill in the expected number of cases that fall into these categories.
- The table labeled **"Answers show on last attempt"** is formatted in the same way as the Expected Values table but is meant to reflect observed results from an experiment.
- In part **(c)**, you are required to **find the test statistic** for the data, which often involves calculating a Chi-square or another relevant statistical measure.
- For part **(d)**, you must determine the **p-value**, which indicates the probability that the observed results are due to chance.
- Finally, part **(e)** asks you to **draw a conclusion** from the test. You need to select whether there is or isn't statistical evidence that migraine pain relief is dependent on receiving acupuncture.
### Additional Notes:
Carefully calculate and cross-verify your expected values and observe the counts before proceeding to calculate the test statistic and p-value. Proper rounding to specified decimal places is crucial for an
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