Should I reject the null hypothesis or fail to reject the null hypothesis?

4. (20 marks) A professor has been teaching an undergraduate course for the last 15 years and has noticed that in the fall term there are more failures than in the same course offered in the winter term. The professor is wondering if this may be due to students being less prepared for the subject matter in the fall than in the winter because more students are taking the prerequisite simultaneously. Before drawing any conclusions though, the professor goes back over all the grades in all classes she taught in the last 15 years and counts the number of students that passed or failed. She then also records who had and had not completed the prerequisite first (see Table 4 for the data). On the basis of the last 15 years of data, should the professor conclude that there is a difference in pass and failure rates depending on whether the prerequisite was done or not? Use the alpha of 0.05 and carry out all the steps of hypothesis testing to answer the hypothesis. Table 4. Course completion based on prerequisite PREREQUISITE OUTCOME Completed prior Simultaneously 60 Fail 120 515