Statistics
Apr
08,
2015

How do I know when to use the t-test instead of the z-test?

Just about every statistics student I've ever tutored has asked me this question at some point. When I first started tutoring I'd explain that it depends on the problem, and start rambling on about the central limit theorem until their eyes glazed over. Then I realized, it's easier to understand if I just make a flowchart. So, here it is!

Basically, it depends on four things:

- Whether we are working with a mean (for example, "37 students") or a proportion (e.g., "15% of all students").
- Whether or not we know the
*population*standard deviation ($\sigma$). In real life we usually don't, but statistics courses like to contrive problems where we do. - Whether or not the population is normally distributed. This is mainly important when dealing with small sample sizes.
- The
*size*of our sample. The magic number is usually 30 - below that is considered a "small" sample, and 30 or above is consi...