Exploring the CLT via simulation

This application exercise explores the Central Limit Theorem (for means) via simulation.

Tasks

1. Load the following dataset:

pops <- read.csv("https://stat.duke.edu/~mc301/data/pops.csv")

Assume each column of this dataset represents a population. Each team will work with one of the populations (columns):

• DasCrew: normal (normal)
• MeanGirls: somewhat right skewed (some_rs)
• StatSheep: very left skewed (very_ls)
• TheStatian: some wonky distribution (wonky)

2. Treat the column assigned to you as your distribution, and create sampling distributions of sample means from samples of sizes

• \(n = 10\)
• \(n = 50\)
• \(n = 200\)

Use 15,000 samples.

Note that sampling distributions are created by taking random samples, with replacement, from the original population. (Just like the bootstrap sample, except from the population instead of a sample.)

Make histograms and normal probability plots of these distributions. You should know how to make histograms by now, and remember from the slides that you can make normal probability plots using

ggplot(data = name_of_dataframe, aes(sample = name_of_variable)) +
  geom_point(stat = "qq")

3. Describe the shapes of these distributions, and calculate the centers (mean) and the spreads (standard deviation). Compare these to shapes, centers, of spreads of parent population distributions from (1).

4. [Optional] If time allows (i.e. your team finishes before others), repeat the same exercise with the other populations (columns) as well.

Tips

You do not need to write a function, but if you do, it will be really easy to repeat for other sample sizes (or other populations).

Submission instructions

Your submission should be an R Markdown file in your team App Ex repo, in a folder called AppEx_09.

Due date

End of class today

Watch out for…

merge conflics on GitHub – you’re working in the same repo now!

Issues will arise, and that’s fine! Commit and push often, and ask questions when stuck.