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