The nonparametric statistics textbook by Hollander and Wolfe (1999) discussed a study on a social skills training program for alcoholics. A sample of male alcoholics was randomly split into two groups. The control group received traditional treatment. The treatment group received the traditional treatment plus a class in social skills training. Every two weeks for a year after the treatment, subjects indicated the quantity of alcohol they consumed during that period. The summary response was the total alcohol intake for the year (in centiliters).
a. Suppose the researchers planned to conduct a one-sided test and believed that the response variable could be highly skewed to the right. Why might they prefer to use the Wilcoxon test rather than a two-sample t test to compare the groups?
b. The data were
Controls: 1042, 1617, 1180, 973, 1552, 1251, 1151, 1511, 728, 1079, 951, 1319
Treated: 874, 389, 612, 798, 1152, 893, 541, 741, 1064, 862, 213
Show how to find the ranks and the mean ranks for the two groups.
c. MINITAB reports the results shown in the output below. Report and interpret the P-value.
d. Report and interpret the confidence interval shown in the output.
MINITAB output

Median 1165.5 798.0 control treated 11 Point estimate for ETAI-ETA2 is 435.5 95.5 Percent CI for ETA-ETA2 is (186.0, 713.0) Test of ETA1=ETA2 vs ETA1 > ETA2s significant at 0.0009 12