Sample Means

Calculate the mean and standard deviation of the sampling distribution of a sample mean  $\overline{x}$   and interpret the standard deviation. 

Explain how the shape of the sampling distribution of  $\overline{x}$   is affected by the shape of the population distribution and the sample size. 

Goto this site: http://onlinestatbook.com/stat_sim/sampling_dist/

Click Begin

Take samples (lots!) and figure out if you can ever get a skewed distribution

Be sure to try varieties of the initial distribution from the pull down menu

If the population distribution is Normal, then so is the sampling distribution of  $\overline{x}$   

This is true no matter what the sample size is.

If the population distribution is not Normal, the sampling distribution of  $\overline{x}$   will be approximately Normal when the sample size is sufficiently large $n\ge30$  

If the distribution is normal, awesome, proceed as normal

If the distribution is not normal, then take a large sample - at least 30

That means if our sample is larger than 30, we can assume the distribution will be normal. One more awesome.

In a nutshell, that is the Central Limit Theorem