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. 69 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 98 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= 0.05.

Pain Free: Yes Pain Free: No Total

Treatment 14 55 69

Control 9 89 98

Total 23 144 167

a) What is the correct null hypothesis?

• H0:p1 p2p3p4
• H0: Migraine pain relief is dependent on receiving acupuncture.
• H0:p1=p2=p3=p4
• H0: Migraine pain relief is independent on receiving acupuncture.

b)Expected ValuesPain Free: YesPain Free: No

Treatment

Control

Answers show on last attemptPain Free: YesPain Free: No

Treatment

Control

c) Find the test statistic, round answer to at least 3 decimal places.

d) What is the p-value? Round answer to at least 3 decimal places

e) What is the correct conclusion?

• There is statistical evidence that migraine pain relief is dependent on receiving acupuncture.
• There is no statistical evidence that migraine pain relief is dependent on receiving acupuncture.