9.7: Formula Review

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    9.4 Distribution Needed for Hypothesis Testing

    Sample size Test 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 Full Hypothesis Test Examples

    Test statistic for a hypothesis test of proportions:
    \[
    Z_c=\frac{\mathrm{p}^{\prime}-p_0}{\sqrt{\frac{p_0 p_0}{n}}}
    \notag \]

    This page titled 9.7: Formula Review was last modified on Mon, 17 Mar 2025 07:04:33 GMT and 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 the style and standards of the LibreTexts platform.