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 15 62 6 78 21 140 Treatment Control Total 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 P4 Ho Migraine pain relief is dependent on receiving acupuncture Total 77 84 161 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 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