Suppose that you have a two-way table with the following row and column totals.

The observed values in the cells must be counts, which are nonnegative integers. Calculate the expected counts for the cells under the assumption that the two variables are independent. Based on your calculations, explain why it is impossible for the test statistic to have a value of zero.

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Variable 1 Total 120 205 175 500 Variable 2 Total 165 140 195