Download Statistics William Knapp Study Guide 9 Central Limit Theorem Today

Statistics
William Knapp
Study Guide 9
Central Limit Theorem
Today we’re going to talk about one of the most important theorems in all of statistics. This theorem
will allow us to compute statistics based on normally distributed populations for samples from nonnormally distributed populations. To understand what the central limit theorem states, it will be
useful to understand what sampling distributions are. Since most of the tests we'll be performing are
tests of sample means, we'll focus on sampling distributions of the mean.
What is the central limit theorem?
(http://www.statisticalengineering.com/central_limit_theorem.htm or check out this video from the
Khan Academy: http://www.khanacademy.org/math/statistics/v/central-limit-theorem)
What is a sampling distribution? (http://www.psychstat.missouristate.edu/introbook/sbk19.htm)
What is a sampling distribution of the mean?
(http://onlinestatbook.com/2/sampling_distributions/samp_dist_mean.html)
What is the mean of the sampling distribution of the mean? (see the above link)
What is the variance of the sampling distribution of the mean? (see the above link)
What is the standard error of the mean (SEM)?
(http://onlinestatbook.com/2/glossary/standard_error.html & http://explorable.com/standarderror-of-the-mean.html)
So why does the formula for a z-test include the SEM in the denominator instead of the standard
deviation of the population? (Try to answer this on your own. If you can't figure it out, rewatch the
end of the lecture.)