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 151 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 66 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 85 patients in the control group 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 a = 0.05. Pain Free: Pain Free: Total Yes No Treatment 19 47 66 Control 7 78 85 Total 26 125 151 a) What is the correct null hypothesis? Ho: Migraine pain relief is independent on receiving acupuncture. Ho: Migraine pain relief is dependent on receiving acupuncture. b) Fill in the expected values, round answers to at least 2 decimal places. Expected Values Pain Free: Yes Pain Free: No Treatment Control c) Find the test statistic, round answer to 1 decimal place. x* =
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 151 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 66 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 85 patients in the control group 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 a = 0.05. Pain Free: Pain Free: Total Yes No Treatment 19 47 66 Control 7 78 85 Total 26 125 151 a) What is the correct null hypothesis? Ho: Migraine pain relief is independent on receiving acupuncture. Ho: Migraine pain relief is dependent on receiving acupuncture. b) Fill in the expected values, round answers to at least 2 decimal places. Expected Values Pain Free: Yes Pain Free: No Treatment Control c) Find the test statistic, round answer to 1 decimal place. x* =
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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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 151 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control.
- **Treatment Group:** 66 patients received acupuncture specifically designed to treat migraines.
- **Control Group:** 85 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 = 0.05.
#### Contingency Table
| | **Pain Free: Yes** | **Pain Free: No** | **Total** |
|------------------|--------------------|-------------------|-----------|
| **Treatment** | 19 | 47 | 66 |
| **Control** | 7 | 78 | 85 |
| **Total** | 26 | 125 | 151 |
### Questions:
**a) What is the correct null hypothesis?**
- \(H_0\): Migraine pain relief is independent of receiving acupuncture.
- \(H_1\): Migraine pain relief is dependent on receiving acupuncture.
**Correct Answer:** \(H_0\): Migraine pain relief is independent on receiving acupuncture.
**b) Fill in the expected values, round answers to at least 2 decimal places.**
| **Expected Values** | **Pain Free: Yes** | **Pain Free: No** |
|---------------------|--------------------|-------------------|
| **Treatment** | | |
| **Control** | | |
**c) Find the test statistic, round answer to 1 decimal place.**
\[ \chi^2 = \]
**d) What is the p-value? Round answer to at least 3 decimal places.**
\[ \text{P-value} = \]
The p-value is...](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce846d56-76a2-4878-8900-9a6a8b90abc9%2Fb030145f-0e29-461b-a169-09666b3153a2%2Fc7a43ma.jpeg&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 151 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control.
- **Treatment Group:** 66 patients received acupuncture specifically designed to treat migraines.
- **Control Group:** 85 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 = 0.05.
#### Contingency Table
| | **Pain Free: Yes** | **Pain Free: No** | **Total** |
|------------------|--------------------|-------------------|-----------|
| **Treatment** | 19 | 47 | 66 |
| **Control** | 7 | 78 | 85 |
| **Total** | 26 | 125 | 151 |
### Questions:
**a) What is the correct null hypothesis?**
- \(H_0\): Migraine pain relief is independent of receiving acupuncture.
- \(H_1\): Migraine pain relief is dependent on receiving acupuncture.
**Correct Answer:** \(H_0\): Migraine pain relief is independent on receiving acupuncture.
**b) Fill in the expected values, round answers to at least 2 decimal places.**
| **Expected Values** | **Pain Free: Yes** | **Pain Free: No** |
|---------------------|--------------------|-------------------|
| **Treatment** | | |
| **Control** | | |
**c) Find the test statistic, round answer to 1 decimal place.**
\[ \chi^2 = \]
**d) What is the p-value? Round answer to at least 3 decimal places.**
\[ \text{P-value} = \]
The p-value is...
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