How Many Per Arm
Two groups are compared with a two-sided z-test at significance level 0.05, using equal group sizes and a known common standard deviation σ = 10. The test should have power 80% to detect a true difference in means of 4. Use z = 1.96 (for the 2.5% tail) and z = 0.84 (for 80% power), and the formula n = 2 σ² (z_a + z_b)² / δ² per group. What is the required sample size per group? Give an integer.
Related problems & prerequisites
Worth solving first
- Power of a Ten-Flip Test 2.0/10
- Power of a One-Sided Uniform Test 2.0/10
Source: Standard two-sample sample-size formula from clinical-trial design. Statement written for AxiomIQ.