At a university, 15 juniors and 20 seniors volunteer to serve as a special committee that requires 8 members. A lottery is used to select the committee from among the volunteers. Suppose the chosen students consists of six juniors and two seniors.
(a) For a test of homogeneity, what are the expected counts?
(b) If the selection had been random, what is the probability of the committee having exactly two seniors?
(c) If the selection had been random, what is the probability that the committee would have two or fewer seniors?
(d) Is there evidence that the selection was not random?