9: In which of the following cases is a person most likely to maintain
  attitude change?

C: A college student goes through severe initiation to get into a
    sorority.

    Correct.
The principle involved in this answer is called justification of effort, and was originally demonstrated in a study by Aronson & Mills (1959).  In this 1959 study, two groups were asked to participate in a sex discussion.  One group received a severe initiation and the other received a mild initiation.  The actual discussion turned out to be very boring.  Subjects receiving the severe initiation liked the discussion far better than those subjects who received the mild initiation.  The reason hypothesized for this result is the subjects receiving were motivated (by dissonance) to justify their severe initiation, by enjoying the boring discussion, while those who received the mild initiation did not have to justify their effort, because their initiation did not require much effort.  In question 9 severe initiation will cause this student to justify her effort, thus she will like the sorority a lot.  She will probably maintain this attitude change, because she will always be forced to justify to herself why she put in so much effort in joining the sorority.