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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

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