Track 7 · Estimation and Confidence Intervals · Lesson 5 of 10
Interpreting confidence correctly
Explain what the confidence level of an interval means — coverage of a procedure over repeated samples — and recognise the common wrong readings.
A report says “95% CI: 34.3 to 40.3 minutes”, and a manager concludes there is a 95% chance the true mean is in that range. It sounds harmless, but it is wrong, and the same muddle leads people to over-trust single studies and to misread what a replication should show.
In the frequentist framework used throughout this track, the parameter is a fixed number. It does not move. What moves is the sample — and therefore the interval computed from it. Before we collect data, the endpoints and are random, and the procedure is designed so that
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It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- State the meaning of a confidence level as the long-run coverage of a procedure
- Explain why a computed interval has no 95% probability of containing the fixed parameter
- Spot the common misreadings: probability for μ, individual values, replication predictions
- Use simulation and exact calculation to check whether a method delivers its promised coverage