# 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 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.

This page titled 3.6: Putting it all Together Using the Classical Method 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; a detailed edit history is available upon request.