Makes sense to me. It can be a little tricky to figure out what they mean by "statistically significant", but if you think about it in terms of the normal distribution (or whatever distribution you are using to test a hypothesis), what p-values and "significance" levels are saying, is that if you get a result that falls OUTSIDE of our significance level, or a test statistic that has a p-value way small (smaller than say a .05 significance level), then the only way the null hypothesis could possibly be true, is if you got that result by some divine miracle considering the chances are SO small. Therefore there has to be another explanation (that null hypothesis is false is one). Generally this means that the sample you have either didn't come from the same population that the null hypothesis is representing. The interpretation is of couse different depending on what kind of test you are running. Overall though you've have it right.