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3.6: Putting it all Together Using the Classical Method

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    Putting it all Together Using the Classical Method

    To Test a Claim about μ when σ is Known

    • Write the null and alternative hypotheses.
    • State the level of significance and get the critical value from the standard normal table.
    • Compute the test statistic.

    \[z=\frac {\bar {x}-\mu}{\frac {\sigma}{\sqrt {n}}}\]

    • Compare the test statistic to the critical value (Z-score) and write the conclusion.

    To Test a Claim about μ When σ is Unknown

    • Write the null and alternative hypotheses.
    • State the level of significance and get the critical value from the student’s t-table with n-1 degrees of freedom.
    • Compute the test statistic.

    \[t=\frac {\bar {x}-\mu}{\frac {s}{\sqrt {n}}}\]

    • Compare the test statistic to the critical value (t-score) and write the conclusion.

    To Test a Claim about p

    • Write the null and alternative hypotheses.
    • State the level of significance and get the critical value from the standard normal distribution.
    • Compute the test statistic.

    \[z=\frac {\hat {p}-p}{\sqrt {\frac {p(1-p)}{n}}}\]

    • Compare the test statistic to the critical value (Z-score) and write the conclusion.

    Table \(PageIndex{1}\). A summary table for critical Z-scores.

    Two-sided Test

    One-sided Test

    Alpha (á)

    á

    Z á

    0.01

    2.575

    2.33

    0.05

    1.96

    1.645

    0.10

    1.645

    1.28

    To Test a Claim about Variance

    • Write the null and alternative hypotheses.
    • State the level of significance and get the critical value from the chi-square table using n-1 degrees of freedom.
    • Compute the test statistic.

    \[\chi^2 = \frac {(n-1)S^2}{\sigma^{2}_{0}}\]

    • Compare the test statistic to the critical value and write the conclusion.

    This page titled 3.6: Putting it all Together Using the Classical Method was last modified on Mon, 08 Jan 2024 09:04:04 GMT and is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Diane Kiernan (OpenSUNY) via source content that was edited to the style and standards of the LibreTexts platform.