Suppose that you collect data on two categorical variables and summarize the results in a 2 × 2 table of counts such as the following:

Your goal is to decide if the data provide strong evidence that Group A and Group B diff er with regard to the long-run proportion of success.

a. Is it possible to investigate this question even when the sample sizes of the two groups are different? Explain your answer, as if to a friend who is skeptical.
b. Is it possible to investigate this question even when the sample sizes of the two groups are both less than 10? Explain your answer, as if to a friend who is skeptical.

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Group A Group B Success Failure