Unfortunately the writer's own understanding of statistics is flawed. For example sample size has not much to do with population size but a lot to do with effect size. For example to demonstrate that a chemical is fatal often a sample size of 1 is sufficient. Population comes into play if there is a large variance of the effect relative to the average size of the effect. You need a good statistical sampling of the population to study the variance but even here sample size if not determined by population size.