In some situations where the expected counts are too small, as in Exercise 38, 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 is a new table displaying the same data, but combining €œMarginal€ and €œPoor€ into a new category called €œBelow Average.€

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 groups and state an appropriate conclusion.

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Men Women Excellent G0od 12 Average 14 Below Average 12