- The $t$ procedures assume that our data come from an SRS and will give trustworthy conclusions only if this condition is met.
- If your sample size is less than 15, the $t$ procedures yield trustworthy conclusions only if you can reasonably assume that your data comes from a normal distribution, that is, if the distribution appears to be symmetric with one peak and no outliers. If your data are obviously skewed or if there are any outliers, it is not advisable to use the $t$ procedures. Non-parametric methods may be more advisable: try the Wilcoxon Signed Rank Test.
- If your sample size is 15 or larger, the $t$ procedures can be trusted if there are no outliers and the distribution is not obviously skewed.
- If your sample size is 40 or larger, you may use $t$ procedures even if your distribution appears to be skewed.

Data | |

Sample data goes here (enter numbers in columns): | |

Null Hypothesis: | $H_0: \mu=\mu_0=$ |

Alternative Hypothesis: | $H_a:\mu$ $\mu_0$ |

Level of Significance: | $\alpha=$ |

Sample Size: | $n=$ |

Degrees of Freedom: | $df=n-1=$ |

Square Root of Sample Size: | $\sqrt{n}=$ |

Sample Mean: | $\overline{x}=$ |

Sample Standard Deviation: | $s=$ |

Critical $t$ Value: | $t^{*}=$ |

$t$ statistic: | $t=$ |

$p\mbox{-value}=$ |