| When sampling from a: | Test statistic | Test statistic |
| Small Sample (n<30) | Large Sample (n>30) | |
| Normal distribution with known variance | z-statistic | z-statistic |
| Normal distribution with unknown variance | t-statistic | t-statistic* |
| Nonnormal distribution with known variance | not available | z-statisitc |
| Nonnormal distribution with unknown variance | not available | t-statistic* |
*The z-statistic is theoretically acceptable here, but use of the t-statistic is more conservative.
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