4.2.4—Mean confidence intervals

A confidence interval has the form estimate ± critical value × standard error. It gives a range produced by a method that captures the fixed population parameter in a stated proportion of repeated samples.

Choose the correct normal or t-based model and use the sample size and variability assumptions. A 95% interval is about the method’s long-run coverage, not a 95% probability attached to the already fixed mean.

If x̄=20 and the margin is 1.5, report (18.5,21.5) in the measurement units and explain the confidence level.

A wider interval is not automatically worse: it may reflect higher confidence or a smaller sample. The interval does not contain 95% of individual observations.