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Hypothesis Testing & Power

Type I/II errors, rejection regions, and statistical power

Visualize a one-tailed z-test. The null N(0,1) and alternative N(δ√n, 1) distributions overlap. Move the sliders to see how significance level, effect size, and sample size trade off.

Critical value z*
1.645
Power (1−β)
86.3%
Type II error β
13.7%
δ√n (ncp)
2.739
Null H₀: N(0,1) Alt H₁: N(δ√n, 1) Type I error (α) Type II error (β) Power
z* = 1.64-4-3-2-101234567test statistic z0.000.100.200.300.40density

One-tailed z-test. Null: N(0,1). Alternative: N(δ√n, 1). Increase n or δ to raise power.

Hypothesis Testing & Power — Statistics Labs · hbar.university