# 9.5: Chapter Formula Review


## 9.3 Distribution Needed for Hypothesis Testing

Sample sizeTest statistic
< 30
($$\sigma$$ unknown)
$$t_{c}=\frac{\overline{X}-\mu_{0}}{s / \sqrt{n}}$$
< 30
($$\sigma$$ known)
$$Z_{c}=\frac{\overline{X}-\mu_{0}}{\sigma / \sqrt{n}}$$
> 30
($$\sigma$$ unknown)
$$Z_{c}=\frac{\overline{X}-\mu_{0}}{s / \sqrt{n}}$$
> 30
($$\sigma$$ known)
$$Z_{c}=\frac{\overline{X}-\mu_{0}}{\sigma / \sqrt{n}}$$
Table $$\PageIndex{6}$$ Test Statistics for Test of Means, Varying Sample Size, Population Known or Unknown

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