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Statistics LibreTexts

Section 6

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.

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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.