I claim that I make 80% of my basketball free throws. To test my claim, you ask me to shoot 20 free throws. I make only 8 of the 20. “Aha!” you say. “Someone who makes 80% of her free throws would almost never make only 8 out of 20. So I don’t believe your claim.” Is this reasoning statistically valid

Although 8/20 is statistically deviant from 80%, one session seems to be too small a sample to disbelieve the claim.