A pharmaceutical manufacturer undertakes a study to prove the effectiveness of its diet pill. The company selects a random sample of 50 young women aged 18 to 25, and puts them on a weight-loss program. Half of them (randomly selected) are given the diet pill, and half are given a placebo. Total weight loss, after 30 days, is recorded for all the participants in the study. The distributions of weight loss are non-normal, but both are skewed to the right, with some unusually high weight losses recorded. The rank sum of the weight losses with the diet pill is 700, and the rank sum of the weight losses with the placebo is 575. Do these data prove that the diet pill is effective? Use α = 4%.
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