Statistics Foundation · Lesson 4.2
Confidence intervals.
Confidence intervals turn a sample estimate into a range of plausible population values. This lesson explains interval estimation, margin of error, confidence level, long-run coverage, interpretation and the most common mistakes.
Lesson route
Build intervals from sampling uncertainty.
Lesson 4.1 introduced standard error. Lesson 4.2 shows how standard error becomes an interval around an estimate, and why confidence must be interpreted through repeated sampling.
0–15 min
Why intervals are needed
Understand why a point estimate alone is incomplete and why inference needs uncertainty around the estimate.
15–35 min
Estimate plus uncertainty
Build the confidence interval structure: estimate ± critical value × standard error.
35–60 min
Margin of error
Study how standard error and confidence level combine to form the margin of error.
60–85 min
Long-run confidence
Understand confidence level as long-run coverage across repeated samples, not probability that one fixed interval contains the parameter.
85–110 min
Interpretation mistakes
Avoid common errors such as saying there is a 95% probability that the true mean lies in this specific interval.
110–135 min
Precision and design
Explore how sample size, variability and confidence level affect interval width and study precision.
Mastery checklist
Students should interpret intervals as uncertainty ranges from a repeated-sampling method.
Explain why point estimates need uncertainty.
Construct intervals using estimate ± critical value × SE.
Calculate margin of error and interval width.
Explain how sample size affects interval width.
Explain how confidence level affects interval width.
Interpret 95% confidence as long-run coverage.
Avoid probability misinterpretations of one realised interval.
Discuss practical meaning, not only statistical significance.