A migraine is a particularly painful type of headache, which patients sometimes wish to treat with , , acupuncture. To d'eterrnine 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 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 (All-ais, 2011). ' (round answers to 2 decimal places) - _n " m n a) What percent of patients in the treatment group were pain free 24 hours after receiving acupuncture? lit. . b) What percent of patients in the control group were pain free after 24 hours? _ l% c) At first glance, does acupuncture appear to be an effective treatment for migraines? Explain your reasoning. ' yes, because more individuals in the treatment group Were pain-free after 24 hours no, because there were fewer people in the treatment group ' yes, because a higher percentage of individuals in the treatment group were 'painefree after 24 hours ' ' no, because more than half of the individuals in the treatment group still experience pain 24 hours- later ' d) Do the data provide convincing evidence that there is a real .pa-in neduction for those-patients in the 7 treatment group? Or do you think that the observed difference might just be due to chance. ' _- Yes, 23% is much higher than 4% ' It is impossible to tell merely by comparing the sample .prtiportions because the difference could be the result of random error in our sample I Submit