Idea that might or might be relevant depending on how smart / advanced your group is.

You could introduce some advanced statistical methods and use it to derive results from everyday life, a la Bayes and mammography.

If you can show some interesting or counter intuitive results (that you can't obtain with intuition) it would give the affective experience you want, and if they want to do scientific research, the more they know about statistics the better.

Statistics are also a good entry door for rationalist thinking.