Grades again In some situations where the expected cellcounts are too small, as in the case of the grades givenby Professors Alpha and Beta in Exercise 39, we cancomplete an analysis anyway. We can often proceed aftercombining cells in some way that makes sense and alsoproduces a table in which the conditions are satisfied.Here we create a new table displaying the same data, butcalling D’s and F’s “Below C”:a) Find the expected counts for each cell in this newtable, and explain why a chi-square procedure is nowappropriate.b) With this change in the table, what has happened tothe number of degrees of freedom?c) Test your hypothesis about the two professors, andstate an appropriate conclusion. Prof. Alpha Prof. BetaA 3 9B 11 12C 14 8Below C 12 3

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.