Independence condition

I’m kind of confused on how we can conclude independence in a sampling distribution if the sample size is <10% of the population. Can someone please explain the reasoning behind this?


Let’s say we are randomly selecting people and asking them whether or not they plan to vote for candidate X. The same way the probability of drawing a black card changes the more cards you draw without replacement, the probability of selecting someone who plans to vote for candidate X changes each time someone new is chosen. This difference in the number of people who plan to vote for candidate X after each new selection would be detrimental to our sample if the population was not large enough. For example, when choosing 50 people out of several thousand in a large city, this difference would not be significant enough to effect our survey in any meaningful way. Now, if we were to select 25 people from a school of only 150, then this difference would be significant enough to effect our survey in a negative way. Hope this clears things up!

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