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 161 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 77 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 84 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: Yes Pain Free: No Total Treatment Control Total 15 62 77 6 21 78 84 140 161 a) What is the correct null hypothesis? Ho: Migraine pain relief is independent on receiving acupuncture. Ho: P1 P2 P3 P4 Ho: P1 P2 P3 = PA 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 Treatment Control Pain Free: Yes Pain Free: No Answers show on last attempt Treatment Control Pain Free: Yes Pain Free: No 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