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

The independent t-test is the appropriate statistical test for comparing the means of two independent samples because it is specifically designed to assess whether there is a statistically significant difference between the average values of two separate groups. In scenarios where each sample represents different groups or conditions that are not related, the independent t-test compares the means calculated from each group, takes into account the variability within the samples, and determines the likelihood that the observed difference occurred by chance.

This test assumes that the samples are drawn from normally distributed populations and that the two groups have similar variances. It is ideal for situations where researchers want to analyze the effects of an intervention or a difference between groups, such as comparing the effectiveness of two different medications on patient outcomes.

In contrast, the paired t-test is intended for comparing means from two related groups, such as measurements taken from the same subjects at two different times. The chi-square test evaluates categorical data for independence, while ANOVA (Analysis of Variance) is used for comparing means across three or more groups. Each of these tests serves a distinct purpose in data analysis, making the independent t-test the suitable choice for comparing means of two independent samples.