Migraine and Acupuncture: A migraine is aparticularly painful type of headache, which patients sometimeswish to treat with acupuncture. To determine whether acupuncturerelieves migraine pain, researchers conducted a randomizedcontrolled study where 166 patients diagnosed with migraineheadaches were randomly assigned to one of two groups: treatment orcontrol. 67 patients in the treatment group received acupuncturethat is specifically designed to treat migraines. 99 patients inthe control group received placebo acupuncture (needle insertion atnon-acupoint locations). 24 hours after patients receivedacupuncture, they were asked if they were pain free. Results aresummarized in the contingency table below. Test to see if migrainepain relief is dependent on receiving acupuncture. Use ?? =0.05.
| Pain Free: Yes | Pain Free: No | Total |
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| Treatment | 16 | 51 | 67 |
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| Control | 4 | 95 | 99 |
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| Total | 20 | 146 | 166 |
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a) What is the correct null hypothesis?
- H0H0: p1?p2?p3?p4p1?p2?p3?p4
- H0H0: p1=p2=p3=p4p1=p2=p3=p4
- H0H0: Migraine pain relief is dependent on receivingacupuncture.
- H0H0: Migraine pain relief is independent on receivingacupuncture.
b) Fill in the expected values, round answers to at least 4decimal places.
| Expected Values | Pain Free: Yes | Pain Free: No |
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| Treatment | | |
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| Control | | |
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| Answers show on last attempt | Pain Free: Yes | Pain Free: No |
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| Treatment | | |
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| Control | | |
|---|
c) Find the test statistic, round answer to at least 4 decimalplaces.
d) What is the p-value?
e) What is the correct conclusion?
- There is no statistical evidence that migraine pain relief isdependent on receiving acupuncture.
- There is statistical evidence that migraine pain relief isdependent on receiving acupuncture.
