Confidence Interval Simulator

Inference Core Capture the Parameter

Watch repeated random samples construct horizontal confidence intervals. Count how many intervals span the fixed truth (μ) to understand what 95% confidence actually means.

Total Studies 0 Independent random samples

Captured True μ 0 Intervals containing parameter

Missed True μ 0 Intervals failing to capture

Empirical Coverage — Target: 95%

1. Population Distribution & Sampling Parameters

Select Population Shape:

Sample Size per Study (\(n\)): 30

Notice how larger \(n\) narrows the confidence intervals without altering coverage rate.

Confidence Level (\(1 - \alpha\)):

Determines the theoretical target capture frequency.

Constructed Intervals (Green = Spans μ, Red = Misses μ)

● Spanned True μ ● Missed True μ - - True Parameter (μ)