I found the lab about Randomized Response Surveys, from chapter 6, interesting. This lab has the reader explore how to get accurate data from a survey and how to evaluate that data.
An important mathematical term introduced in this lab would be bias, which is the difference between an estimate’s expected value and the true value to be estimated. Expected value would actually be another term defined in this chapter, there is actually a fair amount of vocabulary.
A good example question from this lab is without doing any simulations, guess the general shape of the functional relation between Pr(Heads) for the penny and the SD of the estimate. How do you think the estimator will behave if Pr(Heads) is near 0? near 1? Record your guess in the form of a sketch of a graph of SD (theta) as a function of theta = Pr(Heads).
I think the general nature of statistics, having to adjust for unexpected circumstances and how you apply logic and patterns to those circumstances is what fascinates me about this lab.