# 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.

*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.