As I understand it, the Central Limit Theorem (CLT) guarantees that the
distribution of sample means is normally distributed regardless of the
distribution of the underlying data as long as the sample size is large
enough and the population standard deviation is known.
It seems to me that most statistics books I see over optimistically invoke
the CLT not when n is over 30 and the population standard deviation is
known but anytime n is over 30. This seems inappropriate to me or am I
overlooking something?
When the population standard deviation is not know (which is almost all the
time) it seems to me that the Student t (t) distribution is more
appropriate. However, t requires that the underlying data be normal, or at
least not too non-normal. My expectations is that most data sets are not
nearly "normal enough" to make using t appropriate.
So, if we do not know the population standard deviation and we cannot
assume a normal population, what should we be doing-as opposed to just
using the CLT as most business statistics books do?
Ronny Richardson
Ronny Richardson
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