If I have two sets of random samples and I'd like to test whether there is some difference or not between them (or if one is better than the other) I'd test the null hypothesis $H_0: \mu_1 = \mu_2$ with a one-tailed test. So if it turns out that the null hypothesis is rejected on some significance level I could say the one has a significantly higher mean than the other (It was some time ago I studied this so please correct me if I'm wrong).
But what if I have more than two sets of random samples, is it possible to do a similar (I would assume: set of) test(s) so that I could draw the conclusion that one or some of has a significantly higher mean than the others.
If possible you someone please direct me to some keywords, papers and/or briefly explain how it's done.
Thanks in advance!