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Statistics LibreTexts

Section 6

  • Page ID
    2888
  • 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.

    4820.png

    Table 4. A summary table for critical Z-scores.

    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.