Study Design
The name of the one-sample t test tells us the general research design of studies in which this statistic is selected to test hypotheses. We use the one-sample t test when we collect data on a single sample drawn from a defined population. In this design, we have one group of subjects, collect data on these subjects, and compare our sample statistic (M) to the population parameter (μ). The population parameter tells us what to expect if our sample came from that population.

If our sample statistic is very different (beyond what we would expect from sampling error), then our statistical test allows us to conclude that our sample came from a different population. Again, in the one-sample t test, we are comparing the mean (M) calculated on a single set of scores (one sample) to a known population mean (μ).