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The Central Limit Theorem specifically calls out a sample mean to be following normal distribution (for \(\displaystyle n>=30\) ), But I am referring to certain text, and it is calculating \(\displaystyle z\) values for sample \(\displaystyle skewness\) and sample \(\displaystyle kurtosis\) assuming that these follow Normal distribution. Is it correct?
In short, if we take unlimited number of samples each of size \(\displaystyle n\) (where \(\displaystyle n>=30\) ) then for each sample \(\displaystyle skewness\) and \(\displaystyle kurtosis\) will vary. So these are random variables. The question is -- Is the sampling distribution of these random variables Normal?. And if it is, what is the mean \(\displaystyle \mu\) and standard deviation \(\displaystyle \sigma\) for that?
In short, if we take unlimited number of samples each of size \(\displaystyle n\) (where \(\displaystyle n>=30\) ) then for each sample \(\displaystyle skewness\) and \(\displaystyle kurtosis\) will vary. So these are random variables. The question is -- Is the sampling distribution of these random variables Normal?. And if it is, what is the mean \(\displaystyle \mu\) and standard deviation \(\displaystyle \sigma\) for that?