In a study reported in the September 24, 2007, of Archives of Internal Medicine, German researchers stated a study conducted on 162 German adults suffering from chronic low-back pain. These subjects were randomly assigned to one of three groups: real acupuncture, sham acupuncture, or conventional therapy. Researchers found that 47% of subjects in the real acupuncture group improved compared to 44% in the sham acupuncture group and 27% in the conventional therapy group.
a. What kind of test (z-, t-, or chi-square) would be appropriate for testing whether the improvement proportions differ significantly among these three groups? (No explanation is needed.)
b. Report the appropriate degrees of freedom for this test.
c. The p-value turns out to be very close to .05. Summarize the conclusion you would draw.