Researchers studied subjects who had pneumonia and classified them as being in one of two groups: those who were given medical therapy that is consistent with American Thoracic Society (ATS) guidelines and those who were given medical therapy that is inconsistent with ATS guidelines. Subjects in the "consistent" group were generally able to return to work sooner than were subjects in the "inconsistent" group. A Wilcoxon-Mann-Whitney test was applied to the data; the P-value for the test was 0.04. For each of the following, say whether the statement is true or false and say why.
(a) There is a 4% chance that the "consistent" and "inconsistent" population distributions really are the same.
(b) If the "consistent" and "inconsistent" population distributions really are the same, then a difference between the two samples at least as large as the difference that these researchers observed would only happen 4% of the time.
(c) II a new study were done that compared the "consistent" and "inconsistent" populations, there is a 4% probability that H0 would be rejected again.