The general rule of thumb for when to use a t score is when your sample:
You must know the standard deviation of the population and your sample size should be above 30 in order for you to be able to use the z-score. Otherwise, use the t-score.
Like z-scores, t-scores are also a conversion of individual scores into a standard form. However, t-scores are used when you don’t know the population standard deviation; You make an estimate by using your sample.
$T = (X – μ) / [ s/√(n) ]$
where s = standard deviation of sample data
If you have a larger sample (over 30), the t-distribution and z-distribution look pretty much the same. Therefore, you can use either. That said, if you know σ, it doesn’t make much sense to use a sample estimate instead of the “real thing”, so just substitute σ into the equation in place of s:
T = (X – μ) / [ σ/√(n) ]
This makes the equation identical to the one for the z-score; the only difference is you’re looking up the result in the T table, not the Z-table. For sample sizes over 30, you’ll get the same result.