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8.6: Chapter 8 Formulas

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    Hypothesis Test for One Mean

    Use z-test when σ is given.

    Use t-test when s is given.

    If n < 30, population needs to be normal.

    Type I Error-

    Reject H0 when H0 is true.

    Type II Error-

    Fail to reject H0 when H0 is false.

    Z-Test:

    H0: μ = μ0

    H1: μ ≠ μ0

    \(Z=\frac{\bar{x}-\mu_{0}}{\left(\frac{\sigma}{\sqrt{n}}\right)}\)

    TI-84: Z-Test

    t-Test:

    H0: μ = μ0

    H1: μ ≠ μ0

    \(t=\frac{\bar{x}-\mu_{0}}{\left(\frac{s}{\sqrt{n}}\right)}\)

    TI-84: T-Test

    z-Critical Values

    Excel:

    Two-tail: \(z_{\alpha / 2}\) = NORM.INV(1–\(\alpha\)/2,0,1)

    Right-tail: \(z_{1-\alpha}\) = NORM.INV(1–\(\alpha\),0,1)

    Left-tail: \(z_{\alpha}\) = NORM.INV(\(\alpha\),0,1)

    TI-84:

    Two-tail: \(z_{\alpha / 2}\) = invNorm(1–\(\alpha\)/2,0,1)

    Right-tail: \(z_{1-\alpha}\) = invNorm(1–\(\alpha\),0,1)

    Left-tail: \(z_{\alpha}\) = invNorm(\(\alpha\),0,1)

    t-Critical Values

    Excel:

    Two-tail: \(t_{\alpha / 2}\) =T.INV(1–\(\alpha\)/2,df)

    Right-tail: \(t_{1-\alpha}\) = T.INV(1–\(\alpha\),df)

    Left-tail: \(t_{\alpha}\)= T.INV(\(\alpha\),df)

    TI-84:

    Two-tail: \(t_{\alpha / 2}\) = invT(1–\(\alpha\)/2,df)

    Right-tail: \(t_{1-\alpha}\) = invT(1–\(\alpha\),df)

    Left-tail: \(t_{\alpha}\) = invT(\(\alpha\),df)

    Hypothesis Test for One Proportion

    H0: p = p0

    H1: p ≠ p0

    \(Z=\frac{\hat{p}-p_{0}}{\sqrt{\left(\frac{p_{0} q_{0}}{n}\right)}}\)

    TI-84: 1-PropZTest

    Rejection Rules:

    • P-value method: reject H0 when the p-value ≤ \(\alpha\).
    • Critical value method: reject H0 when the test statistic is in the critical region (shaded tails).

    This page titled 8.6: Chapter 8 Formulas was last modified on Sun, 12 Mar 2023 17:54:56 GMT and is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Rachel Webb via source content that was edited to the style and standards of the LibreTexts platform.