Confidence intervals
Draw repeated samples and discover which intervals capture the true mean.
Sample size and precision
1 question · No time limit
Example
Example
Which method produces narrower intervals?
This controlled simulation has population mean μ = 40 and known standard deviation σ = 12. Each sample contains n independent normal observations. Each interval is sample mean ± z × σ/√n. Samples are independent between repetitions.
1. Predict
| Method A | Method B | |
|---|---|---|
| Sample size n | 16 | 36 |
| Multiplier z | 2 | 2 |
Interval: x̄ ± zσ/√n
Make a prediction first. It is not scored.
2. Test your idea
Draw samples to see intervals move around the fixed population mean.
The chart shows the 12 latest intervals per method. Solid intervals contain μ; dashed intervals miss it. Simulation estimates do not determine the scored answer.
Try the controls, then check your solution.
Why?
The full width is 2 × z × σ/√n. Method A has width 12; method B has width 8. The width does not depend on the particular sample mean.
Under the stated model, repeated-sample coverage is approximately 95.4% for A and 95.4% for B. A finite simulation may differ from these long-run values.
Coverage describes the procedure across repeated samples. Once an interval is calculated, the fixed population mean is either inside it or outside it. The confidence level is not a probability assigned to that one fixed interval.
Revisit your prediction
The full width is 2 × z × σ/√n. Method A has width 12; method B has width 8. The width does not depend on the particular sample mean.
Keep exploring the experiment.
Change one thing
3. Change the rules
A linked challenge. This answer is not scored.
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How this data is usedHelp
Try the controls, then check your solution.
Your first checked solution is recorded. You can keep experimenting afterwards.
About this practice
Learn a method
Read confidence as coverageDraw repeated samples and discover which intervals capture the true mean.
For a broader mix of practices, explore the statistics practice test. Membership is required to start a test.
Report a problem
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is used