z-test and t-test
Sampling and inference · Mathematics
Study notes
Q: n = 16, x̄ = 105, s = 20. Test H₀: μ = 100 vs H₁: μ ≠ 100 at α = 0.05. σ unknown, small n: use t with df = 15. t = (105-100)/(20/4) = 5/5 = 1. Critical t(15, 0.025) = ±2.131. |1| < 2.131: fail to reject H₀. Not enough evidence μ differs from 100!