Ok, since you know so much about testing hypothesis, i will prove you that 10 is enough to check a percentage around 50%:
Sync works if you have 2 syncers in your team means p = 52.5%. Out of 10 there should be 5.25 adamant ones. Let's be generous and say we'd accept everything from 2 to 9 adamant pkmn, so that it shouldn't be looked after this hypothesis. Otherwise we say the hypothesis is wrong. We call the number of adamant pokemon we get k.
Chance that this Hypothesis is true and we have a result out of the accepted interval (significance) is (P(k=0)+P(k=1)+P(k=10) = 0.87%. THIS IS WORTH LOOKING AFTER!
Usually you can't calculate the likelyhood of the 2nd kind (which is the one for hypothesis is wrong, but you accept it because just by chance you got nice results) because you don't know anything about the real likelyhood if your hypothesis is wrong. However, in this case we know it, it is p=1/25=4% then, since there are 25 natures and no sync is active. So this chance is 1-(P(k=1)+P(k=9)+P(k=10))=5,82%, this time with p=4% instead of 52.5% of cause.
If you still say there is no validity or reliability on this test, then you are a bonobo.
PS: Get educated before acting clever!