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I am currently using a formula I got from a Qualtrics blog post to calculate the sample I require for a survey for the mean to be meaningful/reflect the population mean, as follows:

https://i.stack.imgur.com/s7KAm.jpg

My survey has a large Std.dev (1.8), which I use instead of assuming a 0.5 Std.dev. This formula does not seem to take into consideration the population size (>10 000), however.

Is there an alternate formula to calculate required sample size with a known population size (but an unknown population std.dev)?

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Population size is irrelevant unless the sample is a large portion of the population, which is clearly not the case here. There is a finite population correction: $FPC = \sqrt{\frac{N-n}{N-1}}$

where N is population size and n is sample size, but this is so close to 1 in your case that it can be ignored.

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  • $\begingroup$ Out of interest and possible future application, what would one then do with the FPC value (which in my case is 0,98)? $\endgroup$
    – The_Dude
    Jul 24, 2017 at 12:39
  • $\begingroup$ One would multiply the sample size by its inverse. $\endgroup$
    – Peter Flom
    Jul 24, 2017 at 12:49
  • $\begingroup$ So n * (1/FPC)? $\endgroup$
    – The_Dude
    Jul 24, 2017 at 13:37

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