I think there are a couple of points of hypothesis testing that may be helpful. First, review the definition of p value: It's the probability of getting data as extreme as the observed values assuming that the null hypothesis is true. Conceptually, one could stop at this point, without moving on to making a hard decision about whether the null hypothesis can be "rejected." Second is the idea that the observed values you are examining are sampled from some populations. You can't examine the populations; you just have these samples to consider. So, it may be that your samples are not identical (and perhaps your test returns a p value: 0.05 < p < 1). But the question the hypothesis test is trying to address is, Is this good evidence against the populations from which the samples were drawn being identical? It's not addressing hypotheses about the observed data. In fact, it would be trivially easy to address some question about the observed data. For example, we could calculate the exact mean of the observed data, and so on. But that's not the question of interest. When you are looking up the hypotheses tested by a statistical test, you should be finding the hypotheses stated in terms of the populations from which the samples are drawn, but often authors use simple or imprecise language.