1-A T-test and a Z-test are almost similar in theory, but have a different application mechanism. The major difference with these two is the size of the sample applied in each case. The t-test is appropriate for smaller samples. Any sample less that 30 units are best analysed using the t-test, while beyond 30 units require a z-test. A z-test is also better if the standard deviation is not known.
T tests are used to compare a given mean to the mean of the given population; it can be applied to either individual values or ones that are paired. The T test can be helpful when you do not know the standard deviation and is best utilized when your sample size is smaller (n<30 sample size) (Lango, 2015). For example, in a Z test you must know the standard
2-Z-test- implies a hypothesis test which ascertains if the means of two datasets are different from each other when variance is given. It is based on normal distribution with a known population variance and a large sample size >30 units
T-test- refers to a type of parametric test that is applied to identify how the means of two sets of data differ from one another when variance is not given. It is based on student T distribution when the population is unknown and the sample size is smaller, <30 units.
Reference
Difference Between t-test and z-test (with Comparison Chart) – Key Differences. (2018, March 10). Retrieved from https://keydifferences.com/difference-between-t-test-and-z-test.html
3-Yes, in theory these two test are common with differences only setting in when applying them. Both used in hypothesis setting, the z-test is better applicable when the standard deviation is known, and when dealing with a larger sample size. A z-test is better to use when dealing with a larger sample size than of over 30. A t-test is better when the sample size is less than 30, and when dealing with an unknown standard deviation
