Confidence Intervals: Certainty vs Precision
Confidence Intervals: Certainty vs Precision
HIV/AIDS Prevalence Research in South Africa
Study Details: Sample size = 1,000 people | Sample prevalence = 12.9% | Population parameter (assumed) = 13.7%
Confidence Level Lower Bound Upper Bound Margin of Error (±) Interval Width Certainty Precision
90% 11.7% 14.1% ±1.2% 2.4% Lower certainty
(90% confident)		 Higher precision
(Narrower range)
95% 11.2% 14.6% ±1.7% 3.4% Moderate certainty
(95% confident)		 Moderate precision
(Balanced range)
99% 10.5% 15.3% ±2.4% 4.8% Higher certainty
(99% confident)		 Lower precision
(Wider range)
⚖️ The Trade-off: Higher certainty comes at the cost of lower precision (wider intervals)

📋 Key Insights

90% CI: We're 90% confident the true prevalence is between 11.7% and 14.1% (most precise, least certain)
95% CI: We're 95% confident the true prevalence is between 11.2% and 14.6% (standard choice, good balance)
99% CI: We're 99% confident the true prevalence is between 10.5% and 15.3% (most certain, least precise)
All intervals contain the assumed population parameter of 13.7%, validating our sample