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This question already has an answer here:

I used the following formula to calculate the sample size. n = (Z2 K p (1-p)) / i2; (k = 2, Z = 1.96, p = expected proportion, i = 0.03) I noticed that the sample size is not related to the population size, it means whatever the population size is small or large, the sample size is still the same! I do not assimilate? My idea is that if the population size is important, certainly the size of the sample increases and vice versa. Is there a requirement to use this formula?

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marked as duplicate by whuber Nov 13 '14 at 15:10

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  • $\begingroup$ Formulas of this nature, which are based on several approximations, are applicable when both the following hold: (1) $np$ is not "too small" (a lower threshold of $5$ is usually cited); and (2) the population size is substantially larger than $n$ (how much larger depends on how certain you are about $p$, but we might start being concerned when the population is less than about $10n$). Note that neither of these conditions can be checked until you have actually computed $n$! $\endgroup$ – whuber Nov 13 '14 at 15:10
  • $\begingroup$ Please do not alter your post in order to respond directly to comments (unless the alterations reflect improvements to the question itself): instead, post comments here. I have rolled your post back to its original version. You attempted to say that you are interested in "representativeness," but that's a completely different issue than the questions you originally raised about sample size and population size. Would you care to clarify this? $\endgroup$ – whuber Nov 13 '14 at 18:14
  • $\begingroup$ Thank you. If I try to determine the sample size is in order to get an accurate representation of the whole of the target population, in orderto generalize the results to the entire population. A sample is a set of individuals representative of a population. What I am trying to understand why the size of the population is not included in the formula for calculating of sample size(n = Z² K * p * (1-p) / i²). Because my idée, if i have a large size population certainly, the sample size will be as large and vice versa. $\endgroup$ – houneida Nov 13 '14 at 19:08
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The population size does matter, but, unless the sample size is a large proportion of the population, it matters so little that it can be ignored.

If N is the population size and n is the sample size, then the correction factor is

$ \sqrt{\frac{N-n}{N-1}} $

so, e.g. if you were doing polling for a national election, it would make essentially no difference if you took 300 people from a city, state or country.

This is counterintuitive, but correct.

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