Estimation and Confidence Intervals
Estimate unknown quantities and state the uncertainty honestly.
Point and interval estimates, margins of error, intervals for means, proportions, paired and two-sample differences, sample-size planning and bootstrap intervals — with a coverage simulator that shows what 95% confidence really means.
Lessons
- 1Point estimates and their propertiesUse sample statistics as point estimates of population parameters and judge an estimator by its bias and its variability.25 minFree
- 2The idea of an interval estimateBuild an interval estimate as estimate ± margin of error and explain what makes the interval wider or narrower.20 minMembers
- 3Interval for a mean with known σFind z critical values and build and interpret a z confidence interval for a mean when the population standard deviation is known.25 minMembers
- 4Interval for a mean with unknown σBuild and interpret a t confidence interval for a mean, explain why t replaces z when σ is estimated, and judge when the interval can be trusted.30 minMembers
- 5Interpreting confidence correctlyExplain what the confidence level of an interval means — coverage of a procedure over repeated samples — and recognise the common wrong readings.25 minMembers
- 6Interval for a proportionBuild Wald and Wilson intervals for a proportion, and recognise when the Wald interval fails.30 minMembers
- 7Intervals for differences in meansBuild and interpret confidence intervals for a difference in means from independent samples (Welch) and from paired data.35 minMembers
- 8Interval for a difference in proportionsBuild and interpret intervals for a difference in proportions with the unpooled Wald method and Newcombe's hybrid score method.30 minMembers
- 9Planning sample sizeCalculate the sample size needed for a target margin of error when estimating a mean or a proportion.25 minMembers
- 10Bootstrap intervalsBuild a percentile bootstrap interval by resampling, and judge when the bootstrap can and cannot be trusted.30 minMembers