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Z-tests and T-Tests are both statistical methods used to test different hypotheses and analyze their differences. The Z test is used to decide if two population means are different when they know the variances. The best time to use a Z-test is when the sample size being used is larger than 30 and the population standard deviation is known. A T-test is used examine two population means, a two sample t-test can be used to determine if two samples are different and this test is most commonly used when the variances of two normal distributions are not known and with smaller sample sizes less than 30. The following are some of the differences that can be noted between Z-tests and the T-tests.

Z-tests:

Z-tests will follow normal distribution.
Z-tests require their samples to be moderate to large in size (n>30).
They require certain conditions be reliable tests.
Z-tests are less commonly used.
Z-tests are preferred when standard deviations are available.

T-tests:

T-tests will follow the Student’s T-distribution.
T-tests are more appropriate for smaller sample sizes (n<30).
T-tests are more flexible and adaptable than z-tests.
T-Tests are more commonly used.
Can be used if the population’s standard deviation is not known. 

                                                             References

DifferenceBetween.net. (2010). Difference Between Z-test and T-test. Retrieved from http://www.differencebetween.net/miscellaneous/difference-between-z-test-and-t-test/

Investopedia.com. (2017). Definition of T-test & Z-test. Retrieved from

http://www.investopedia.com/terms/t/t-test.asp

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