Confidence Interval Builder

Overview

The Confidence Interval Builder helps you understand and visualize confidence intervals for different scenarios. A confidence interval provides a range of plausible values for a population parameter. This interactive tool shows how confidence intervals are calculated, demonstrates their coverage properties through simulation, and helps build intuition about what “95% confidence” really means.

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Tips

  • The confidence level (90%, 95%, 99%) refers to the long-run proportion of intervals that capture the true parameter
  • A 95% CI doesn’t mean “95% probability the true value is in this interval” - the true value either is or isn’t in this specific interval
  • Wider intervals (99%) give more confidence but less precision; narrower intervals (90%) are more precise but less confident
  • Watch the simulation: approximately 95% of the intervals should contain the true mean (shown in red)
  • Increasing sample size makes intervals narrower (more precise) while maintaining the same confidence level
  • The intervals that miss the true parameter aren’t “wrong” - they’re the expected 5% that fail by random chance
  • One-sample intervals estimate a single population mean; two-sample intervals estimate the difference between two means
  • For proportions, the interval can never extend below 0 or above 1, which affects the calculation method