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 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 nonacupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below.
(a) What percent of patients in the treatment group were pain free 24 hours after receiving acupuncture? What percent in the control group ?
(b) At first glance, does acupuncture appear to be an effective treatment for migraines? Explain
your reasoning
(c) 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 different might just be due to chance?