🔬 Session 9.2 – Z-Test for Mean (σ Known)

This tool walks through hypothesis testing when the population variance is known. It uses the normal distribution.

🧪 Hypothesis Test Inputs

H₀: μ =    H₁:

Sample mean (x̄):    σ:    n:    α:

📋 Summary Table: Z-Test for Known Variance

Alternative Hypothesis Test Statistic P-Value Rejection Rule
H₁: μ ≠ μ₀ Z₀ = (x̄ − μ₀) / (σ / √n) P = 2[1 − Φ(|Z₀|)] Z₀ > zα/2 or Z₀ < −zα/2
H₁: μ > μ₀ Z₀ = (x̄ − μ₀) / (σ / √n) P = 1 − Φ(Z₀) Z₀ > zα
H₁: μ < μ₀ Z₀ = (x̄ − μ₀) / (σ / √n) P = Φ(Z₀) Z₀ < −zα