The purpose of the Mann-Whitney U test is primarily for:

The Mann-Whitney U test is designed specifically for comparing differences between independent samples. It is a non-parametric test, meaning it does not assume that the data follows a normal distribution, making it useful when the assumptions of parametric tests cannot be met. This test evaluates whether the distribution of scores in one group differs from that of another group, providing insights into the median differences between them without requiring specific distribution characteristics.

In the context of the other options, the paired samples hypothesis testing refers to tests like the paired t-test or Wilcoxon signed-rank test, which compare two related groups rather than independent ones. Assessing variance within a single group is typically done using tests like the one-sample t-test or analysis of variance (ANOVA) for multiple groups. Calculating correlations involves tests such as the Pearson or Spearman correlation coefficients, which measure the strength and direction of a relationship between two continuous variables. Thus, the focus of the Mann-Whitney U test on the differences between independent samples validates why it is the correct purpose among the presented choices.