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 $9 females diagnosed with migraine headaches were randonlly zorigned to one of two groups: treatment or control. 43 patients in the treatment group received soupuncture that is specifically designed to treat migraines. 46 patients in the control group received placebo acupuncture (needle insertion at non-acupoint location), 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below (Allais, 201!). (round answers to 2 decimal places) Pain Free: YesPain Free: No Total Treatment 10 33 43 Control 2 Total 12 77 a) What percent of patients in the treatment group were pain free 24 hours after receiving acupuncture? Proctor b) What percent of patients in the control group were pain free after 24 hours? ") At first glance, does acupuncture appear to be an effective treatment for migraines? Explain your reasoning. Oyes, because a higher percentage of individuals in the treatment group were pain- free after 24 hours yes, because more individuals in the treatment group were pain free after 24 hours Ono, because there were fewer people in the treatment group Ono, because more than half of the individuals in the treatment group still experience pain 24 hours book Ister () Do the data provide convincing evidence that there is a real pain reduction for those patients in the orms treatment group? Or do you think that the observed difference might just be due to charice? It is impossible to tell merely by comparing the sample proportions because the difference could be the result of random error in our sample Yes, 23% is much higher than 4%