1. Sampling Distribution of the Mean
is a random variable whose value depends on which members of the population are selected in the sample.

2. Facts about the Sampling Distribution of the Mean
The average value of across all possible samples is , the population mean. Thus, .
The standard deviation of the sampling distribution of is the population standard deviation divided by the .

3. The sample to sample variability in decreases as n increases.
is the standard error of
The sample to sample variability in decreases as n increases.
Large samples are more precise than small samples.

4. If our sample comes from a normal distribution with mean,
If our sample comes from a normal distribution with mean, , and standard deviation, , then
has the standard normal distribution.

5. Central Limit Theorem
If we sample from a population with mean, , and standard deviation, , then
is approximately standard normal for large n.

6. How large does n have to be?
If population is normal or near normal, n can be quite small.
If population is far from normal, the approximation is reasonably good for n=30, most of the time.