Editing Statistics and Statistical Programming (Fall 2020)/pset4 (section)

=== (Recommended) PC6. A simulation === 
Let's conduct a simulation that demonstrates a fundamental principle of statistics. Please see the [https://communitydata.science/~ads/teaching/2020/stats/r_tutorials/w05-R_tutorial.html R tutorial materials from last week] for useful examples that can help you do this.
:* (a) Create a vector of 10,000 randomly generated numbers that are uniformly distributed between 0 and 9.
:* (b) Calculate the mean of the vector you just created. Plot a histogram of the distribution.
:* (c) Create 100 random samples of 2 items each from your randomly generated data and take the mean of each sample. Create a new vector that contains those means. Describe/display the distribution of those means.
:* (d) Do (c) except make the items 10 items in each sample instead of 2. Then do (c) again except with 100 items. Be ready to describe how the histogram changes as the sample size increases. (''Bonus challenge:'' Write a function to complete this part.)

==== Compare and explain the simulation ====
Compare the results from PC6 with those in the example simulation from [https://communitydata.science/~ads/teaching/2020/stats/r_tutorials/w05-R_tutorial.html last week's R tutorial]. What fundamental statistical principle is illustrated by these simulations? Why is this an important simulation for thinking about hypothesis testing?