In some situations the sequence of steps used in t-test can be done using z-scores instead of t-scores. Then such a test is called z-test.
Use: z-test is/can be used in place of t-test when
• The population standard deviation is known which allows the standard error, rather than the estimated SE to be found
• The sample is sufficiently large (n > 200) for the SD to provide a reliable estimate of SE.
Funda: Although there a situations in which a t-test can be used but z-test cannot, there are no situations in which a z-test can be used but a t-test cannot. So t-tests are the most important and widely used of the two.
Note: Source: Page 79; RxPG Biostatistics Buster, Tyagi, Jaypee Publishers.