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 while 46 patients in the control group received placebo acupuncture. 24 hours after patients received acupuncture, they were asked if they were pain free. What are the cases in this data set? What two variables are collected? Tell whether each is categorical or quantitative. What is the appropriate null hypothesis in words? What is the appropriate alternative hypothesis in words? Explain what a Type II error would mean in the context of this problem. The results were reported as statistically significant at the 10% level showing that acupuncture did increase the proportion of patients who were pain free. This conclusion could actually be an error. What type of error might the researcher’s have made? What is the probability of a Type I error in this study? If only 50 women total had volunteered for the study, would the power of the test increase, decrease, or stay the same?