In some situations where the expected cell counts are too small, as in the case of the

Question:

In some situations where the expected cell counts are too small, as in the case of the grades given by Professors Alpha and Beta in Exercise 43, we can complete an analysis anyway. We can often proceed after combining cells in some way that makes sense and also produces a table in which the conditions are satisfied. Here, we create a new table displaying the same data, but calling D's and F's "Below C":

a) Find the expected counts for each cell in this new table, and explain why a chi-square procedure is now appropriate.
b) With this change in the table, what has happened to the number of degrees of freedom?
c) Test your hypothesis about the two professors, and state an appropriate conclusion.