Ineed with this question
two different professors teach an introductory statistics class at a local college. the table below shows the distribution of final grades they reported. we wonder if one of the professors is an “easier” grader.
professor jones professor smith
a 3 9
b 11 12
c 14 8
d 9 4
f 8 4

b. what are the conditions required to use this test? have the conditions been satisfied? explain.

We use a chi-square test of homogeneity, as we have a single categorical variable measured within two different populations.

The requirements for this test are that we have two simple random samples (this is clearly satisfied, given that we are sampling all students who take the class that year) and that the expected value for each cell, defined as the cell's row sum multiplied by the column sum divided by the sum of all values in the dataset, is greater than 5.  This is satisfied simply by testing for each value in the table.

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