Article 5. An introduction to estimation--2: from z to t.

Provided the sample size is large enough (that is, n greater than 100), the z statistic can be used to determine the confidence interval estimation of the population mean even when the sigma is not known. In these cases the estimation of the standard error of the mean is used. The z statistic is also valid when determining the population's proportion based upon a large sample. However, when dealing with smaller samples, the z statistic is replaced by the t statistic. This makes it possible to estimate, in a population with an unknown standard deviation: The probability of getting a sample mean greater than or equal to a particular value The value of a sample mean with a particular probability of occurring The probability of getting a sample mean between two particular values The confidence interval for the estimation of the population mean can also be determined using the t statistic.