Magnets for pain relief 1/5: a randomized, double-blind experiment studied whether magnetic fields applied over a painful area can reduce pain intensity. the subjects were 50 volunteers with postpolio syndrome who reported muscular or arthritic pain. the pain level when pressing a painful area was graded subjectively on a scale from 0 to 10 (0 is no pain, 10 is maximum pain). patients were randomly assigned to wear either a magnetic device or a placebo device over the painful area for 45 minutes. here is a summary of the pain scores for this experiment, expressed as means ± standard deviations: magnetic device(n=29) place device(n=21)pretreatment 9.6 ± 0.7 9.5 ± 0.8posttreatment 4.4 ± 3.1 8.4 ± 1.8change 5.2 ± 3.2 1.1 ± 1.6

a) is there good evidence that the magnetic device is better than a placebo equivalent at reducing pain? let μ1 and μ2 be the mean change in pain for patients given the magnetic device or the placebo device, respectively. state hypotheses for the significant test. b) 18.40 (ex) magnets for pain relief 2/5: give the test statistic, the degrees of freedom and the p-value for the test. use the conservative method and table c. c) 18.40 (ex) magnets for pain relief 3/5: true or false: there is no significant difference between the magnetic device and a placebo in relieving paind) 18.40 (ex) magnets for pain relief 4/5: how much reduction in pain is achieved with the magnetic device? give a 95% confidence interval for the mean difference in pain scores before and after treatment among patients given the magnetic device. use the conservative method and table c. e) 18.40 (ex) magnets for pain relief 5/5: what procedure did you use in the previous problem to find the confidence interval?