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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 a randomized controlled study where 89 females diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 43 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 46 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 (Allais, 2011). (round answers to 2 decimal places) % m. -_ 10 33 Control 2 44 Total 12 . 77 a) What percent of patients in the treatment group were pain free 24 hours after receiving acupuncture? [ % b) What percent of patients in the control group were pain free after 24 hours? % c) At first glance, does acupuncture appear to be an effective treatment for migraines? Explain your reasoning. l 0 yes, because a higher percentage of individuals in the treatment group were pain-free after 24 hours 0 yes, because more individuals in the treatment group were pain-free after 24 hours 0 no, because more than half of the individuals in. the treatment group still experience pain 24 hours later 0 no, because there were fewer people in the treatment group d) Do the data provide convincing evidence that there is a real pain reduction for those patients in the treatment group? Or do you think that the observed difference might just? be due to chance? 0 It is impossible to tell merely by comparing the sample proportions because the difference could be the result of random error in our sample O Yes, 23% is much higher than 4%