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The standard population error of the sampling distribution when we know the population standard deviation is equal to $σ_M = σ/\sqrt n$, or is it, $S_m = σ/\sqrt n$?

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    $\begingroup$ please be more specific what you're trying to ask. Are you trying to distinguish between the standard error of the mean versus the true standard deviation of the sample mean? $\endgroup$ Apr 6 '13 at 18:46
  • $\begingroup$ As both your formulae are the same, are you just asking whether to use a Greek or non-Greek letter to represent it? Also what do you mean by "population error"? $\endgroup$ Apr 6 '13 at 21:48
  • $\begingroup$ Oh, I mean the standard error of the sampling distribution when we know the population standard deviation is equal to _________________. $\endgroup$
    – Luna
    Apr 6 '13 at 22:55
  • $\begingroup$ It would not be a sample estimate if $\sigma$ is known. So if by $S_m$ you mean a sample estimate then it is not that. $\endgroup$ Jun 17 '18 at 21:53
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If you know the population standard deviation, the standard error would be $\sigma_M$, since you would base it off the population parameter, $\sigma$. It would be designated $S_M$ or, probably more typically, $S_\bar{X}$, when based off the sample standard deviation.

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