ABSTRACT
One such statistic that can be used to determine if two means are different is the Z-test. This statistic does have some limitations and, in this context, it is rarely used. The primary limitation is the assumption that the population variance is known. In most cases, the entire population is not known. Instead, a sample from the population is used. This test can be used when sample sizes are large enough, which is seldom the case in planned experiments. Before the widespread use of computers, it used to be, as a rule of thumb, that sample sizes greater than 30 from a normally distributed population were sufficient to use the Z-test.
