Wilcoxon-Mann-Whitney as an alternative to the t-test

The two sample t-test is one of the most used statistical procedures. Its purpose is to test the hypothesis that the means of two groups are the same. The test assumes that the variable in question is normally distributed in the two groups. When this assumption is in doubt, the non-parametric Wilcoxon-Mann-Whitney (or rank sum ) test is sometimes suggested as an alternative to the t-test (e.g. the Wikipedia page on the t-test), which doesn't rely on distributional assumptions. But is this necessarily a good 'replacement'?

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