Part of the mistake here is in interpreting the p value as being a measure of anything really meaningful. P<0.05 doesn't mean 1 in 20 are wrong. It does mean

Part of the mistake here is in interpreting the p value as being a measure of anything really meaningful. P<0.05 doesn't mean 1 in 20 are wrong. It does mean that in the narrow confines of the definition of the statistical model used, it is possible that 1 in 20 would be explainable by the null hypothesis. It is not, in any way a measure of reality. It is a guess at how accurately you've modeled the system, how accurate your priors are, and so forth.