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I was watching a lecture video on hypothesis test from Khan Academy. At 4m 26s of the video, the lecturer defines standard error. Here he says that 'We don't know the standard deviation of the population, but the sample standard deviation is a good estimation, when the sample size is large enough'. To me it sounds odd. The standard error is defined as a sample standard deviation over square root of the sample size. There's no reason to talk about the population standard deviation. Am I wrong?

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  • $\begingroup$ You quote a formula for a standard error, not a definition. In an answer at stats.stackexchange.com/a/18609/919, I introduce the idea of the standard error from basic principles, using no mathematics. Perhaps that answers your question? $\endgroup$ – whuber Apr 13 at 15:35
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There is no standard deviation of the population mean, since it is a fixed constant and constants have no standard deviation (if you really want to define one, it would have to be 0, unless you go onto a Bayesian framework).

However, there is a population standard deviation: the standard deviation of the distribution from which we draw our sample.

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