Which statistical test would be appropriate for comparing the means of two independent groups?

The independent t-test is the appropriate statistical method for comparing the means of two independent groups because it specifically evaluates whether there is a statistically significant difference between the means of these two different groups. This test operates under the assumption that the two groups are unrelated and that the data is normally distributed within each group, making it suitable for the analysis of continuous variables.

In practical applications, you would use this test when you have two separate samples, such as comparing the mean blood pressure readings between two different groups of patients, ensuring that there is no pairing between the observations of the two groups.

The paired t-test, in contrast, is designed for situations where the two samples are related, such as before-and-after measurements on the same subjects, making it unsuitable for the independent group context. One-way ANOVA is used when comparing means across three or more groups, rather than just two. Lastly, the chi-square test evaluates relationships between categorical variables and does not apply to mean comparisons of continuous data.