When using a one-sample t-procedure to construct a confidence interval for the mean of a finite population, a condition is that the population size be at least 10 times the sample size. The reason for the condition is to ensure that

When constructing a confidence interval, we want to make sure that the data we are obtaining are independent of each other. In smaller populations, having a large sample will impact the true mean significantly. In larger populations, the samples will generally be below 10%.