Observed statistic
x̄ = 0.31
Raw difference x̄ - μ₀ = 0.310.
Statistics Simulation
Hypothesis Testing Learning Lab
Understand Type I error, Type II error, power, p-values, and test decisions visually.
Sampling Distribution Under H₀
Decision shading is evaluated under H₀ in sample-mean units; the observed marker sits at x̄.
H₀ distributionRejection regionp-value area
Critical value
xcrit = −0.28, 0.28
Boundary for the selected α and alternative.
p-value
0.028
About 2.8% this extreme if H₀ were true.
Decision
Reject H₀
Because p ≤ α (0.028 ≤ 0.05).
Decision Logic
p-value approach: p = 0.028 <= α = 0.05, so reject H₀. Critical-value approach: x̄ = 0.31 is outside the critical boundaries −0.28 and 0.28, so reject H₀.