Question

A randomized, double‑blind experiment studied whether magnetic fields applied over a painful area can reduce pain intensity. The subjects were 5050 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 00 to 1010 ; (where 00 is no pain, 1010 is maximum pain.)

Patients were randomly assigned to wear either a magnetic device or a placebo device over the painful area for 4545 minutes. A summary is given of the pain scores for this experiment, expressed as means ±± standard deviations.

	Magnetic device (?=29)(n=29)	Placebo device (?=21)(n=21)
Pretreatment	9.6±0.79.6±0.7	9.5±0.89.5±0.8
Post‑treatment	4.4±3.14.4±3.1	8.4±1.88.4±1.8
Change	5.2±3.25.2±3.2	1.1±1.61.1±1.6

(a) Is there good evidence that the magnetic device is better than a placebo equivalent at reducing pain? Let ?1μ1 and ?2μ2 be the mean change in pain for patients given the magnetic device or the placebo device, respectively. State the hypotheses for the appropriate test.

a. ?0:?1−?2=4.1 vs ??:?1−?2≠4.1H0:μ1−μ2=4.1 vs Ha:μ1−μ2≠4.1

b. ?0:?1≤?2 vs ??:?1>?2H0:μ1≤μ2 vs Ha:μ1>μ2

c. ?0:?1−?2=0 vs ??:?1−?2=4.1H0:μ1−μ2=0 vs Ha:μ1−μ2=4.1

d. ?0:?1=?2 vs ??:?1>?2H0:μ1=μ2 vs Ha:μ1>μ2

e. ?0:?1=?2 vs ??:?1≠?2H0:μ1=μ2 vs Ha:μ1≠μ2

f. ?0:?1−?2=4.1 vs ??:?1−?2>4.1H0:μ1−μ2=4.1 vs Ha:μ1−μ2>4.1

g. ?0:?1=?2 vs ??:?1<?2

Give the test statistic and the ?P‑value for the test.

a. ?=1.15,0.10<?<0.20t=1.15,0.10<P<0.20

b. ?=5.95,0.0005<?<0.05t=5.95,0.0005<P<0.05

c. ?=5.95,?<0.0005t=5.95,P<0.0005

d. ?=1.15,0.20<?<0.30t=1.15,0.20<P<0.30

Is there significant difference between the magnetic device and a placebo in relieving pain?

a. There is no evidence that the magnetic device is better than a placebo at relieving pain in this population, on average.

b. There is extremely strong evidence that the magnetic device is better than a placebo at relieving pain in this population, on average.

c. There is significant evidence that the magnetic device is better than a placebo at relieving pain among the study participants.

d. There is some moderate evidence that the magnetic device is better than a placebo at relieving pain in this population, on average.

(b) How much reduction in pain is achieved with the magnetic device? Select the correct 95%95% confidence interval for the mean difference in pain scores before and after treatment among patients given the magnetic device.

a. 3.2 to 5.63.2 to 5.6

b. 3.8 to 6.63.8 to 6.6

c. 4.2 to 6.24.2 to 6.2

d. 4.0 to 6.44.0 to 6.4

What procedure did you use for this confidence interval?

a. The matched pairs ?t procedure

b. The two‑sample ?t procedure

c. The one‑sample ?t procedure

d. None of the options are correct.

Answer 1