Page three returns to the Therapeutic Touch story to discuss the power of a test. The Normal density tool provides a visualization of power that can help students understand this sometimes confusing topic. Page four recalls the data on couples, this time examining ages, and shows that we can test for a difference between the means of two paired groups using the same t-test. Paired data, such as in this example, have the advantage of a natural null hypothesis. This is a good point to be sure that students are focused on practical applications.
Students sometimes focus on the process of testing hypotheses, forgetting the underlying meaning.
The issue they should focus on is still understanding the world from data. Our point of view on choosing between t and z is that people who use computers or modern calculators should choose t-based procedures regardless of the sample size. Computers and calculators have no trouble finding t values for large degrees of freedom, and the smooth transition from t to Normal as the df grows takes care of itself. The only time when a z-based method is preferred is when you know that you have a Normal population, you have a small sample size, and you know the population standard deviation. We know of no such situation in the real world.