Interactive Inference Studio

Hypothesis Testing Lab

Explore Z-tests, t-tests, and one-way ANOVA by generating data, watching sampling distributions respond in real time, and seeing how p-values, critical regions, and decisions move together.

Single-file HTML Offline ready Interactive sampling Interactive inference

Learning Focus

Core Tests

Z, t, F

Switch among one-sample, independent, paired, and ANOVA designs.

Visual Logic

Curves + data

Critical regions, p-value shading, and sample plots stay linked.

Controls

Test Setup

One-sample Z

Hypothesis Test

Significance α

0.050

Tail Direction

Show confidence interval

Data Generation

Visualization

Distribution + Sample View

Acceptance region Critical / p-value region Observed statistic

Synthetic data is regenerated from the controls unless a CSV is loaded.

Results

Interpretation Panel

Awaiting sample

Z = (x̄ − μ) / (σ / √n) Live values appear here after the first sample is generated.

Test Statistic

—

Observed Z / t / F value

p-value

—

Probability of a result at least this extreme under H₀

Degrees of Freedom

—

Depends on the chosen test

Critical Value

—

Threshold based on α and tail direction

Decision

Generate a sample to begin.

The lab will compare the observed test statistic and p-value against your chosen α.

Confidence Interval

—

Intervals help connect estimation and hypothesis testing.

Type I / Type II Intuition

Type I error risk is controlled by α: currently 0.050.

Type II error depends on the true effect size, variance, and sample size. The lab estimates power from the current settings.

Quantity	Value	Meaning

Sampling Log	Statistic	Decision

Hypothesis Testing Lab

Distribution + Sample View

Standard normal curve

Histogram and sample mean

t-test vs ANOVA side-by-side

Which test should you use?