# Criteria for selecting the appropriate test statistic

When sampling from a: | Test Statistic | |
---|---|---|

n < 30 | 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-statistic |

Nonnormal distribution with unknown variance | not available | t-statistic* |

** t-statistic is more conservative*

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