When testing for a single population mean: A Student's t-test should be used if the data come from a simple, random sample and the population is approximately normally distributed, or the sample siz...When testing for a single population mean: A Student's t-test should be used if the data come from a simple, random sample and the population is approximately normally distributed, or the sample size is large, with an unknown standard deviation. The normal test will work if the data come from a simple, random sample and the population is approximately normally distributed, or the sample size is large, with a known standard deviation.