3.6: 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.

Table \(PageIndex{1}\). 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.