Question

Researchers are interested in the effectiveness of methadone in patients with chronic pain syndromes. The researchers used a scale (0-100, higher numbers indicate higher pain) for maximum pain intensity over the course of the day. Each subject took a 20mg dose of methadone for 5 days, and then took a placebo for 5 days. The following table gives the mean maximum pain intensity scores for the 5 days on methadone and the 5 days on placebo. Do these data provide sufficient evidence at the 0.05 level of significance, to indicate, in general, that pain intensity is LOWER on days when methadone was taken?

subject	Methadone	Placebo
1	29.8	57.2
2	73.0	69.8
3	98.6	98.2
4	58.8	62.4
5	60.6	67.2
6	57.2	70.6
7	57.2	67.8
8	89.2	95.6
9	97.0	98.4
10	49.8	63.2
11	37.0	63.6

Answer 1

subject	Methadone	Placebo	Difference (di)	(di-dbar)2
1	29.8	57.2	-27.4	282.9124
2	73	69.8	3.2	189.8884
3	98.6	98.2	0.4	120.5604
4	58.8	62.4	-3.6	48.7204
5	60.6	67.2	-6.6	15.8404
6	57.2	70.6	-13.4	7.9524
7	57.2	67.8	-10.6	0.0004
8	89.2	95.6	-6.4	17.4724
9	97	98.4	-1.4	84.2724
10	49.8	63.2	-13.4	7.9524
11	37	63.6	-26.6	256.6404
Total			-105.8	1032.212
Mean			-10.58
Standard deviation	9.686975
Test Statistic	3.622378
T	1.812461
pvalue	0.002336

Here, we want to test

H0: The pain intensity is same on days when methadone and placebo was taken

H1:The pain intensity is LOWER on days when methadone was taken than placebo

Since, p-value =0.002336 < 0.05

Therefore, we may reject H0.

Hence, we may conclude that, there is sufficient evidence to claim that the pain intensity is LOWER on days when methadone was taken than placebo.