|1-Sample t||Tests whether the mean of a single population is equal to a target value||Is the mean height of female college students greater than 5.5 feet?|
|2-Sample t||Tests whether the difference between the means of two independent populations is equal to a target value||Does the mean height of female college students significantly differ from the mean height of male college students?|
|Paired t||Tests whether the mean of the differences between dependent or paired observations is equal to a target value||If you measure the weight of male college students before and after each subject takes a weight-loss pill, is the mean weight loss significant enough to conclude that the pill works?|
|t-test in regression output||Tests whether the values of coefficients in the regression equation differ significantly from zero||Are high school SAT test scores significant predictors of college GPA?|
An important property of the t-test is its robustness against assumptions of population normality. In other words, with large samples t-tests are often valid even when the assumption of normality is violated. This property makes them one of the most useful procedures for making inferences about population means.
However, with a small sample size and nonnormal and highly skewed distributions, it might be more appropriate to use nonparametric tests.