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I have found the following statement on the internet concerning the necessary number of samples in the central limit theorem:

In practice, some statisticians say that a sample size of 30 is large enough when the population distribution is roughly bell-shaped. Others recommend a sample size of at least 40. But if the original population is distinctly not normal (e.g., is badly skewed, has multiple peaks, and/or has outliers), researchers like the sample size to be even larger. [1]

I need some references that prove this claim (i.e. scientific papers that actually recomend this sample size of 30 or 40). ¿Do you known any of them?

[1] http://stattrek.com/sampling/sampling-distribution.aspx

Daniel López
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  • 1. "recommend" $\neq$ "prove". Which is it? – Glen_b Aug 02 '16 at 10:27
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    this was answered here: http://stats.stackexchange.com/questions/2541/is-there-a-reference-that-suggest-using-30-as-a-large-enough-sample-size – Anton Aug 02 '16 at 10:32
  • The claim is so vague as to be meaningless. It doesn't specify what would constitute some sufficient approximation to normality, so it's impossible to evaluate whether it's really achieved in some instance. – Glen_b Aug 02 '16 at 10:37
  • The author of the cite claims that statisticians recommend sample sizes of 30, I asked for a prove of this claim, i.e. a reference where a statistician recommends a sample size of 30. – Daniel López Aug 02 '16 at 10:37
  • (on the off chance this reopens) ... How is "statistician" defined? How could someone support a claim like this unless it was precise about what was actually being claimed? – Glen_b Aug 02 '16 at 10:53

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