I am confused about how best to compare means when the sample is small and they are not normally distributed.

I have survey data which measured the mental wellness status of a very small sample of a known population size (~5,000). To report the difference in wellness scores according to different categories (e.g., sex and age), I intended to compute the difference in means and corresponding 95% CIs. However, I can't perform a t-test because the data is not normally distributed.

Discussions regarding the use of Mann-Whitney U Test here clarifies that it is not a test for difference in means or medians but rank sum, would this test be appropriate in my case? My goal is simply to interpret the results to say, for example, that the wellness scores for males were higher than females.

Any guidance/advice would be greatly appreciated.

Average wellbeing scores with 95% CI of the mean

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