Tutoring at Indiana University (IU) in Bloomington, Indiana

Finite math, K201, calculus, and statistics explained

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!

z-test versus t-test flowchart

Basically, it depends on four things:

  1. Whether we are working with a mean (for example, "37 students") or a proportion (e.g., "15% of all students").
  2. 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.
  3. Whether or not the population is normally distributed. This is mainly important when dealing with small sample sizes.
  4. The size of our sample. The magic number is usually 30 - below that is considered a "small" sample, and 30 or above is consi...

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