Cases in which the standard deviation is known a priori are less common. Examples include standardized tests for which the mean and standard deviation are published or data from known probability distributions such as the binomial where the theoretical standard deviation can be calculated.
More commonly, we estimate the standard deviation from the data. Even if the standard deviation is known a priori, assuming it is unknown is not inappropriate; however, it will result in a test with slightly less statistical power.
© 2002, Gary McClelland