Fill out the table below: SUM 21 ~/ 6' 71 ~/ 0' 241 ~/ 6' d' 1139 ~/ The correlation coefficient is (round to three decimal places): r = [:] Find the slope, intercept and correlation coefficient and report them accurately to three decimal places. The regression equation is: y = [:]m + D 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 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 a) What percent of patients in the treatment group were pain free 24 hours after receiving acupuncture? [:1 % 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. C] yes, because more individuals in the treatment group were pain-free after 24 hours C] yes, because a higher percentage of individuals in the treatment group were pain-free after 24 hours C] no, because there were fewer people in the treatment group C] 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 pain reduction for those patients in the treatment group? Or do you think that the observed difference might just be due to chance? D Yes, 23% is much higher than 4% C] It is impossible to tell merely by comparing the sample proportions because the difference could be the result of random error in our sample An opaque bag contains 21 yellow marbles and 11 teal marbles. If two marbles are randomly chosen from the bag at the same time, find the probability that both marbles are teal. Round your answer to four decimal places. :] 4. Find P( -1.2