What are good examples to show to undergraduate students?

I am going to teach statistics as a teaching assistant for the second half of this semester to CS-oriented undergraduate students. Most of the students took the class has no incentive to learn the subject and only took it for major requirements. I want to make the subject interesting and useful, not just a class they learn to get a B+ to pass.

As a pure-math PhD student I knew little on the real-life applied side. I want to ask for some real-life applications of undergraduate statistics. Examples I am looking for are ones (in spirit) like:

1) Showing central limit theorem is useful for certain large sample data.

2) Provide a counter-example that central limit theorem is not applicable (say, the ones following Cauchy distribution).

3) Showing how hypothesis testing works in famous real life examples using Z-test, t-test or something.

4) Showing how overfitting or wrong initial hypothesis could give to wrong results.

5) Showing how p-value and confidence interval worked in (well known) real life cases and where they do not work so well.

6) Similarly type I, type II errors, statistical power, rejection level \alpha, etc.

My trouble is that while I do have many examples on probability side (coin toss, dice toss, gambler’s ruin, martingales, random walk, three prisoner’s paradox, monty hall problem, probability methods in algorithm design, etc), I do not know as many canonical examples on the statistics side. What I mean is serious, interesting examples that has some pedagogical value, and it is not extremely artificially made up that seems very detached from real life. I do not want to give students the false impression that Z-test and t-test is everything. But because of my pure math background I do not know enough examples to make the class interesting and useful to them. So I am looking for some help.

My student’s level is around calculus I and calculus II. They cannot even show the standard normal’s variance is 1 by definition as they do not know how to evaluate the Gaussian kernel. So anything slightly theoretical or hands-on computational (like hypergeometric distribution, arcsin law in 1D random walk) is not going to work. I want to show some examples that they can understand not just “how”, but also “why”. Otherwise I am not sure if I will be proving what I said by intimidation.

Answer

One good way can be to install R (http://www.r-project.org/) and use its examples for teaching. You can access the help in R with commands “?t.test” etc. At end of each help file are examples. For t.test, for example:

> t.test(extra ~ group, data = sleep)

        Welch Two Sample t-test

data:  extra by group
t = -1.8608, df = 17.776, p-value = 0.07939
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -3.3654832  0.2054832
sample estimates:
mean in group 1 mean in group 2 
           0.75            2.33 

>  plot(extra ~ group, data = sleep)

enter image description here

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