Is injecting medical cement effective in reducing pain for people who have suffered fractured vertebrae? The paper €œA Randomized Trial of Vertebroplasty for Osteoporotic Spinal Fractures€ (New England Journal of Medicine [2009]: 569€“578) describes an experiment to compare patients who underwent vertebroplasty (the injection of cement) to patients in a placebo group who underwent a fake procedure in which no cement was actually injected. Because the placebo procedure was similar to the vertebroplasty procedure except for the actual injection of cement, patients participating in the experiment were not aware of which treatment they recceived. All patients were asked to rate their pain at three different times€”3 days, 14 days, and 1 month after the procedure. Summary statistics are given in the accompanying table.

a. Briefly explain why the researchers may have chosen to include a placebo group that underwent a fake procedure rather than just comparing the vertebroplasty group to a group of patients who did not receive any treatment.
b. Construct and interpret a 95% confidence interval for the difference in mean pain intensity 3 days after treatment for the vertebroplasty treatment and the fake treatment.
c. Construct and interpret 95% confidence intervals for the difference in mean pain intensity at 14 days and at 1 month after treatment.
d. Based on the confidence intervals from Parts (b) and (c), comment on the effectiveness of injecting cement as a way of reducing pain for those with fractured vertebrae.

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Pain Intensity Vertebroplasty Group Placebo Group n68 sd 2.8 2.9 2.9 sd 2.9 2.8 3.0 mean mean 3 days 14 days I month 4.2 4.3 3.9 3.9 4.5 4.6