1. A new drug for pain relief is being tested within a given palliative care population. The new drug is being compared to an already approved pain relief drug that is commonly used in providing palliative care to patients who experience chronic severe pain. Assume the patients are asked to rate the pain on a scale from 1 to 10, and the data presented below was obtained from a small study designed to compare the effectiveness of the two drugs. Set up and interpret the results of a Mann-Whitney U test with an alpha of .05.

Pain Rating as Reported by Patients

Old Drug 1 2 2 4 6

New Drug 1 2 2 3 7

Old Drug	New Drug	Total Sample (Ordered Smallest to Largest)	Ranks
Old Drug	New Drug	Old Drug	New Drug
1	1	1	1	1.5	1.5
2	2	2	2	4.5	4.5
2	2	2	2	4.5	4.5
4	3		3		7
6	7	4		8
		6		9
			7		10
				R1=27.5	R2=27.5

1. We reject H₀ in favor of H₁, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 12.5 is greater than the critical U value of 2.
2. We reject H₀ in favor of H₁, which states the two populations are not equal at the alpha equals .05 level because the calculated U value of 10.5 is greater than the critical U value of 2.
3. We fail to reject H₀, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 12.5 is greater than the critical U value of 2.
4. We fail to reject H₀, which states the two populations are equal at the alpha equals .05 level because the calculated U value of 10.5 is greater than the critical U value of 2.