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In a test of the independence of two variables, one of the variables has two possible categories and the other has three possible categories. What will be the critical value of chi-square if the test is to be carried out at the o.025 level? At the 0.05 level?

This is a similar question to the previous where you would have to look up the cumulative probability values for a given value of α and degrees of freedom.
For a 2 by three contingency table, the number of degrees of freedom is (2-1)*(3-1)=2.
For α=0.025, cum.probability=0.975, df=2, Χ²=7.38.
You can get the value for α=0.05 in a similar way.

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