Sample Size Determination

Sample size determination for mean estimation. Formula: n = (Z²σ²)/E², where Z = critical value, σ = population SD, E = margin of error. Example: 95% CI (Z=1.96), σ=20, E=5. n = (1.96² × 20²)/5² = (3.8416 × 400)/25 ≈ 61. For proportions: n = (Z²p(1-p))/E². Example: p=0.5, Z=1.96, E=0.05. n = (1.96² × 0.25)/0.05² ≈ 385. Factors increasing n: Higher confidence level, larger σ, smaller E. Solving: Specify confidence, margin of error, variance. Apply formula. Round up. Exam tip: Larger n provides more precision but costs more. Balance accuracy and resources. Practice: Sample size problems for means and proportions.