Which hypothesis test is appropriate for comparing two sample means?

The two-sample t-test is the appropriate hypothesis test for comparing the means of two independent samples. This statistical test is used when you want to determine if there is a significant difference between the means of the two samples, which can be from different groups or populations.

The two-sample t-test makes a few key assumptions, including that the data from both samples are approximately normally distributed and that they have equal variances (although there are variations of this test that can accommodate unequal variances). The test evaluates whether the means are statistically significantly different from each other based on sample data, calculating a t-statistic that can then be compared to a critical value from the t-distribution based on the degrees of freedom.

In contrast, the two-proportion test is designed for comparing two proportions rather than means. The ANOVA two-way test is used for comparing the means across multiple groups while accounting for two different independent variables. Lastly, the paired t-test is used when comparing means from two related groups (for example, measurements taken from the same subjects before and after a treatment). Therefore, the two-sample t-test is specifically tailored for situations where two independent means need to be compared, making it the correct choice.