t-test?

Hello everyone!

Suppose I have a measurement of a variable for two different groups (of different sizes), coming from non-normal distributions, and I want to day something about their means.

I cannot use an unpaired student t-test because of the non-normalities.

However, for each of the groups I can calulate, say, the 95% conf. interval of their means using t distributions. Then, if the conf. intervals for the two means overlap, can I say that the means are not significantly different (at 95% conf. level)? If so, wouldn't this be equivalent to performing an unpaired student t-test?

(I don't want to use the Mann-Whitney U test, because that tests the medians...)

Thanks!
Diodoo
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