• A confidence interval gives us a range of plausible values for \(\mu\).
  • If the null value is in the interval, then \(\mu_0\) is a plausible value for \(\mu\).
  • If the null value is not in the interval, then \(\mu_0\) is not a plausible value for \(\mu\).

1. State null and alternative hypotheses.
2. Decide on significance level \(\alpha\). Check assumptions (decide which confidence interval setting to use).
3. Find the critical value.
4. Compute confidence interval.
5. If the null value is not in the confidence interval, reject the null hypothesis. Otherwise, do not reject.
6. Interpret results in the context of the problem.

Is the average mercury level in dolphin muslces different from \(2.5\mu g/g\)? Test at the 0.05 level of significance. A random sample of \(19\) dolphins resulted in a mean of \(4.4 \mu g/g\) and a standard deviation of \(2.3 \mu g/g\).