If that probability is sufficiently small, it leads us to doubt the initial claim. Returning to the density tool, we see that it serves as a hypothesis testing tool in much the same was as it is a confidence interval tool. The principal difference is that the null hypothesis provides a parameter value, which can now be used to center the density. Students see hypothesis testing in Data Desk and also simulate tests based on many samples from the same population. They also learn to use the Normal table to perform hypothesis tests.
Students can and do derive the reasoning of significance testing for themselves.
The work to set up this exercise can be traced back to the lesson on Randomness. The reasoning of testing is much more natural to students who have discovered it than to those who have been told, so here again we urge that you let students complete their discovery before telling them how to test hypotheses. This reflects both modern teaching wisdom and the way most statistics software and statisticians actually work. Students are asked to record the number of observations they drew before stating a conclusion and the proportion of red outcomes that they observed. This will allow them to compute a personal P-value corresponding to when their discomfort with the result became great enough to force rejection of the null hypothesis.