A small pilot study is run to compare a new drug for chronic pain to one that is currently available. Participants are randomly assigned to receive either the new drug or the currently available drug and report improvement in pain on a 5-point ordinal scale: 1=Pain is much worse, 2=Pain is slightly worse, 3= No change, 4=Pain improved slightly, 5=Pain much improved. Is there a significant difference in self-reported improvement in pain? Use the Mann-Whitney U test with a 5% level of significance. Please show work.

New Drug: 4 5 3 3 4 2

Standard Drug: 2 3 4 1 2 3

What is R1 (for the new drug group)?

what is R2 (for the standard drug group)?

What is U1 (for the new drug group)?