Sample Size Calculation

Statistics · Axiom Academy

EXAMPLE Sample Size Calculation Determining the required sample size for estimating a population mean A pharmaceutical company wants to estimate the average recovery time (in days) for patients taking a new medication. How many patients should they include in their study? Excellent work! You've completed this sample size calculation example. Here's what we learned: Sample size increases with confidence: Higher confidence levels (e.g., 99% vs 95%) require larger samples to maintain the same margin of error. Precision costs more: Reducing the margin of error (E) requires a quadratically larger sample size due to the squared term in the denominator. Always round up: Sample sizes must be whole numbers, and rounding up ensures we meet our precision requirements. Prior knowledge matters: Having an estimate of the population standard deviation (from pilot studies or literature) is crucial for accurate sample size determination. For proportions: When estimating proportions instead of means, use n = (z² × p × (1-p)) / E² where p is the estimated proportion (use 0.5 for maximum sample size). This approach applies to any study where you need to estimate population parameters with a specific level of confidence and precision!

This is the written version of the interactive lesson above. See the full Statistics course.