Question

Graduate students in a particular academic department take a comprehensive exam, for which there are three possible results: High Pass, Pass, or Fail. A researcher is trying to determine whether the true probabilities associated with these three outcomes are (0.35, 0.45, 0.20) for (High Pass, Pass, Fail). A sample of 200 graduate students was taken. In this sample, 51 received a High Pass, 85 received a Pass, and 64 received a Fail. Using a hypothesis test at alpha=0.05, assess whether the true proportions for each category are as the researcher specified. In addition, the researcher also classified the students as “American” or “International”. The resulting two-way classification table was:

	High Pass	Pass	Fail
American	27	45	36
International	24	40	28

Using a hypothesis test at alpha=0.05, assess whether the result of the test is independent of the ethnic background of the student.

Answer 1