7 The Sampling Distribution of the Mean
Definition: Sampling error
Is the error resulting from using a sample, instead of a census,
to estimate a population quantity.
Definition: Sampling distribution of the mean
The probability distribution of the random
variable 
.
Note: is a random variable, so its value depends on chance.
Theorem: For each random sample of size n from a population with a mean m,
mx = m.
Theorem: For each random sample of size n, from a population with standard
deviation s,
= 
.
Central Limit Theorem: For each random sample of size n ³
30, with parameters m and s,
is approximately normally
distributed with parameters 
=
m and
= .
