When is Unknown In most situations we do not know the population standard deviation. In other words, is unknown. The only option available to us is to approximate with a sample standard deviation, s. To do this we need to substitute s for . When we make this substitution, the standard error of the sampling distribution is estimated by sn The test statistic for a sample mean is T=xsn Note that these equations are very similar to equations introduced in Unit 4.1, but we use a sample standard deviation in place of the population standard deviation. Language Tip: Note that instead of saying "the standard error of the sampling distribution is given by," we say it "is estimated by." We make this change because s is only an approximation of