According to this link:
The general rule of thumb for when to use a t score is when your sample size meets the following two requirements:
- The sample size is below 30
- The population standard deviation is unknown (estimated from your sample data)
In other words, you must know the standard deviation of the population and your sample size must be above 30 in order for you to be able to use the z-score. Otherwise, use the t-score.
Question: Suppose that our sample size is below 30 and that we do know our population standard deviation.
Why not use the z-score? I understand that according to the central limit theorem, with $n < 30$ so low we would have no expectation that our sample estimator would be normal. Does this have something to do with why we should prefer the t-score in this case?