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Measuring each single piece of item can sometimes be unpractical, and that is why statistical methods of solving problems were developed. A sample of the population being measured can be more practical (Taeger & Kuhnt, 2014). T-test and T-test are some of the known statistical hypothesis testing methods that have been developed. A T-test is a method of hypothesis testing that uses a student’s T-distribution when the null hypothesis is true. A T-test is used in testing the mean of a population against a standard or comparing two population means when the standard deviation is not known, and the sample is limited (n<30). The method is easy to use, flexible, adaptable to various circumstances and straightforward (Park, 2015).
A Z-test is used to test the mean of a population versus a standard or to compare two populations’ means with samples that are large (n≥30), whether the standard deviation of the population is known or not (Taeger & Kuhnt, 2014).A Z-test determines the probability that a new set of data will be near the point that a certain score was calculated. A Z-test is usually appropriate over a T-test when the standard deviation of a population is known and when there is a normal distribution. Also, a Z-test is more appropriate when comparing the mean of a sample and a population to know if there is a substantial difference between them. There are fluctuations that can occur in a T-test when using large sample variances and would not be experienced when using the Z-test. For instance, a Z-test would be preferable when comparing the average salaries of male engineers and female engineers (Park, 2015).
ReferencesPark, H. M. (2015). Hypothesis testing and statistical power of a test. Taeger, D., & Kuhnt, S. (2014). Statistical hypothesis testing. Statistical Hypothesis Testing with SAS and R, 3-16.