# 9.5: Chapter Formula Review

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## 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

9.5: Chapter Formula Review is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.