In both the one- and two-tailed versions of the small two-sample t-test, we assume that the means of the two populations are equal. To use a t-test for small (independent) samples, the following conditions must be met:
- The samples must be selected randomly.
- The samples must be independent.
- Each population must have a normal distribution.
A small two sample t-test is used to test the difference between two population means μ1 and μ2 when the sample size for at least one population is less than 30. The standardized test statistic is: