## 10.1 Mechanics of a hypothesis test

This structure is consistent for hypothesis testing even through the specifics of the hypotheis being tested and the test statistics being calculated will differ between types of tests.

- Set up the
**null and alternative hypotheses**in words and notation.- In words: ``The population mean for [what is being studied] is different from [value of \(\mu_0\)].’’ (Note that the statement in words is in terms of the alternative hypothesis.)
- In notation: \(H_0: \mu=\mu_0\) versus \(H_A: \mu \ne \mu_0\) (where \(\mu_0\) is specified by the context of the problem).

Choose the

**significance level**of the test, such as \(\alpha=0.05\).Compute the

**test statistic**, such as \(t_{s} = \frac{\bar{Y}-\mu_0}{SE_{\bar{Y}}}\), where \(SE_{\bar{Y}}=s/\sqrt{n}\) is the standard error.Determine the

**tail(s)**of the sampling distribution where the**\(p\)-value**from the test statistic will be calculated (for example, both tails, right tail, or left tail). (Historically, we would compare the observed test statistic, \(t_{s}\), with the**critical value**\(t_{\textrm{crit}}=t_{\alpha/2}\) in the direction of the alternative hypothesis from the \(t\)-distribution table with degrees of freedom \(df = n-1\).)- State the
**conclusion**in terms of the problem.- Reject \(H_0\) in favor of \(H_A\) if \(p\textrm{-value} < \alpha\).
- Fail to reject \(H_0\) if \(p\textrm{-value} \ge \alpha\). (Note: We DO NOT
*accept*\(H_0\).)

**Check assumptions**of the test (next week).