If we instead wish to make inferences about quantities relating to a finite population this is usually done by imposing an adjustment to the standard tests and confidence intervals called a finite population correction (FPC). Thus, for statistical tests and confidence intervals that deal with model parameters, we are implicitly making inferences about a quantity relating to an infinite population. In statistical models that use parameters for the underlying distributions, these parameters correspond to aspects of the empirical distribution of an infinite population (called a 'superpopulation'). <50), should you give up on this assumption because it results in sample sizes too small to get decent estimates of variability and to check other assumptions such as normality. In the case where you have a small population (e.g. A bit of googling suggests that it refers to making a simple random sample without replacement, if the sample size is above 10% then the observations won't be (approximately) independent, and independence of observations is an assumption stated in most textbooks. The author didn't say where this comes from (at least as far as I could see).

My question is: how important is this assumption and what is the reason for it? I havent seen it mentioned in other introductory stats books.

In an introductory stats book by Nicole Radziwill 'Statistics (the easier way) with R', an assumption used for nearly every statistical test (e.g.t-tets, anova, etc) is that the sample size should not be more than 10% of the population size (where the population size in known).

The ten times rule