What statistical method would be appropriate to compare the average lengths of stay between two different age groups?

Using a T-test is appropriate for comparing the average lengths of stay between two different age groups because it is specifically designed to assess whether there is a statistically significant difference between the means of two independent groups. In scenarios where you have two groups (in this case, two different age groups), a T-test can effectively determine if the average lengths of stay differ between them.

This statistical method works under the assumption that the data is normally distributed and that the variances of the two groups are equal or at least similar. The T-test provides a clear and straightforward approach to ascertain if the means of these two groups are significantly different, which aligns perfectly with the goal of the analysis in question.

In contrast, other methods like the chi-square test are suited for categorical data rather than continuous measures of length of stay. ANOVA is typically used when comparing means across three or more groups, making it unnecessary for just two age groups. Regression analysis, while powerful for understanding relationships and predicting outcomes, is not the suitable choice for a simple mean comparison between two clusters of data in this context.