Final answer:
The correct analysis for two variables that each consist of exactly two categories is a Chi-square test of independence. This test checks the relationship between two categorical variables using a contingency table, ensuring each cell has an expected value of at least five.
Step-by-step explanation:
When both variables consist of exactly two categories, the appropriate analysis would involve a Chi-square test. Specifically, for situations where we aim to assess the relationship or independence between two categorical variables, a test of independence is used. The null hypothesis in a test of independence posits that the two variables are independent of each other. If the data falls into a contingency table where each cell compares observed values to expected values, and these expected values must be at least five, then a Chi-square test of independence is appropriate.
The other options, like ANOVA, are used to compare several group means, and it requires certain assumptions, such as samples being drawn from normally distributed populations with equal variances. Regression analysis is used when you want to predict a numerical outcome from one or more predictor variables, and T-tests are used to compare the means of two groups when working with interval or ratio data.
In this case, with two categories for each variable, a Chi-square test of independence is the correct choice to determine if there is a significant association between the two variables.