
Chapter 8
288
regardless of sample size. A population has a mean
μ
and standard deviation
σ
. If a sample of
size n is drawn from the population, for suf ciently large sample size (n ≥ 30); the sample means
are approximately normally distributed regardless of the shape of the population distribution.
Mathematically, it can be shown that the mean of the sample means is the population mean,
that is,
μ
=
x
and the standard deviation of the sample means is the standard deviation of
the population, divided by the square root of the sample size, that is,
σ
σ
x
n
=
. Central limit
theorem is perhaps the most important theorem in statistical inference. ...