I think “corresponds” would be a better word than “leads to” in the question in the thread title. If you only sample 5 out of 1,000,000, there is a high risk that those 5 don't give a full picture of what's going on…and thus a high risk that if those 5 are good, you will incorrectly accept that the whole population is good. Does that make more sense? Whereas if you have a big sample size – you sample 75 of 100 – then if they're all good, the risk that you would incorrectly accept the whole population as being good isn't very great, since if 3/4 are good, probably all of them are good!
The “leads to” is because if you're OK with incorrectly accepting all of them, then you're not going to bother with sampling all of them. If the 1,000,000 listed in my first example is pennies that are sitting in one specific part of the US mint, then that's $10,000. If you're auditing whether or not the cash they say is there is really there, then inspecting lots of the pennies to ensure they are authentic US pennies is probably not worth the time, since the total cash on hand is probably something like 1,000,000,000, so the materiality of some fake or foreign pennies is not worth the time to check them – just grab a few to make sure they're not quarters and go on to the next thing! So, since you aren't worried about whether the $10k of pennies is exactly right or not, you accept a higher risk of incorrect acceptance, and that will lead to a smaller sample size.
…I didn't read the link Jennifer posted, so here's a second explanation in case it helps anyone. 🙂
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