%% EXAMPLE 1: Create a collection of 1000 samples of N(0,1), each of size 10
%% EXAMPLE 2: Calculate the sample means
%% EXERCISE 1: Calculate and output the average of the sample means
%% EXAMPLE 3: Show the distribution of sample means
%% EXAMPLE 4: Calculate the actual and unbiased sample standard deviations
%% EXERCISE 2: Calculate and output the true SEM of the sample means
% The SEM (Standard Error of the Mean) is the true population standard
% deviation (popStd) divided by the square root of the sample size.
% Statisticians have shown that the actual standard deviation of the
% population of all possible sample means is the original population
% standard deviation divided by the square root of the sample size.
% In most cases, we don't actually know the true standard deviation of
% the original population, but in this case we know it exactly because
% we are creating data.
%% EXAMPLE 5: Calculate the estimated standard error of the mean (SEM) for each sample
%% EXAMPLE 6: Output times the true population mean is above SEM error bar
%% EXERCISE 3: Output times the true population mean is below SEM error bar
% Also find and output the fraction of times the true population mean is
% below the SEM error bar.
%% EXAMPLE 7: Output times true population mean is above 95% confidence interval
%% EXERCISE 4: Output times true population mean below 95% CI error bar
% Also find and output the fraction of times the true population mean is below the 95% CI error bars.
%% EXERCISE 5: Output times true population mean outside 95% CI error bar
%% EXAMPLE 8: Output times actual and unbaised sample stds underestimate pop std