Which test would be appropriate for determining if there is a significant difference between the means of two independent samples?

The T-test for independent means is specifically designed to compare the means of two independent groups to determine if there is a statistically significant difference between them. This statistical test assumes that the data from both groups are normally distributed and have similar variances, allowing for a reliable assessment of the difference in means.

When researchers have two distinct groups, such as comparing the test scores of students from two different classes, the independent T-test provides a method to evaluate whether any observed differences in their means are statistically significant or could have occurred by random chance.

Other tests mentioned, like the T-test for dependent means, are suitable for paired samples where the observations are not independent—such as measuring the same subjects before and after an intervention. The Mann-Whitney U test, while useful for comparing two independent samples, does not assume normal distribution and is better for ordinal data or non-normally distributed interval data. The Wilcoxon signed-rank test is specifically for paired samples as well, focusing on ranked data rather than mean comparisons. Thus, when the aim is to analyze the means of two independent groups, the T-test for independent means is the most appropriate choice.