Wolfram/Mathematica Study of Stand. Dev. Scaling with Sample Number, Z scores, Confidence Intervals

In this video we look at some simulations using Wolfram Cloud/Mathematica to build up some intuition about some ideas from statistics. We look at how samples from two normal distributions add to up to samples from one "larger" normal distribution with a mean that is the sum of the constituent means and with a variance that is the sum of the constituent variances. Next we look at drawing N samples from one normal distribution and computing the mean of those samples. The standard deviation of that mean over samples was seen to scale as N^(-0.5). We moved finally to the concept of confidence interval. Assuming we know the standard deviation of the population from which we are drawing samples (but not the mean of the population), we test the idea that population mean lies on an interval around the sample mean a certain percentage of the time.

[@thomasblum9803]

www1.lasalle.edu/~blum/c152wks/zscore.pdf