The z-test is best used for greater-than-30 samples because, under the central limit theorem, as the number of samples gets larger, the samples are considered to be approximately normally distributed.

Stuart R. Lipsitz, Michael Parzen, Sample Size Calculations for Non-Randomized Studies, Journal of the Royal Statistical Society. Series D (The Statistician), Vol. 44, No. 1 (1995), pp. 81-90 ...