Hint: a sample size of 8 is not statistically significant.
Eight kids are born and three have Down Syndrome. Is there definitely something wrong, or is this the variance in small sample sizes?
If the eight kids were drawn from a random sample, either it was a very unlucky sample or there's something very wrong (such as, the number of kids with down syndrome is increasing, perhaps some disease is increasing the chance of it happening). For example, if you sample 8 random kids in the US today and 3 of them have micro-cephaly, I would definitely suspect that the Zika virus is now very active in the US. Sure, there's a chance you sampled the 8 kids in a very unlucky way, but the probability of that is really small. It would be cause for panic.
There's much more to statistics than "just choose a big sample". These things are actually quantifiable, just read the explanations in the binomial calculator page I pasted earlier...