Testing hypotheses using the t test

Abstract

There is one major problem with using the z test and the normal distribution to test even simple hypotheses. This problemarises, in the case of the test for the significance of a single mean, because we must assume that we know the standard deviationof the variable in the population. Specifically, we must know the population standard deviation in order to estimate the standarderror of the sample mean. In practice, of course, we rarely know the values of any of the population parameters. We only knowthe values of the sample statistics. For many years, statisticians were content to estimate the population standard deviationof a variable using the sample standard deviation of that variable. However, they later discovered that this practice oftenled to incorrect inferences.