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 166 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 75 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 91 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. Pain Free: Yes Pain Free: No Total Treatment 15 60 75 Control 86 91 Total 20 146 166 a) What is the correct null hypothesis? O Họ: p1 + p2 + p3 # P4 O Họ: Migraine pain relief is dependent on receiving acupuncture. O Họ: Migraine pain relief is independent on receiving acupuncture. O Ho: Pi = P2 = p3 = P4 b) Fill in the expected values, round answers to at least 2 decimal places. Expected Values Pain Free: Yes Pain Free: No Treatment Control Answers show on Pain Free: Pain Free: No last attempt Treatment Control Yes 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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