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 = 0.01. Treatment Control Total Pain Free: Yes Pain Free: No 15 51 5 80 20 131 Total 66 85 151 a) What is the correct null hypothesis? Ho: There is no relationship between migraine pain relief and treatment by acupuncture. Ho: There is a relationship between migraine pain relief and treatment by acupuncture. Ho:p1 = P2 = P3 = P4 Ho: P1 P2 P3 ‡ P4 b) What is the correct alternative hypothesis? OHA: There is no relationship between migraine pain relief and treatment by acupuncture. ⒸHA: There is a relationship between migraine pain relief and treatment by acupuncture. HA:P₁ = P2 = P3 = P4 OHA: P1 P2 P3 P4 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

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