Margin of error
Margin of error is the half-width of a confidence interval — the critical value multiplied by the standard error — showing the maximum likely sampling error at a chosen confidence level. A larger sample reduces it.
See it move
A survey of 400 customers finds a mean satisfaction score of 7.2 with a standard deviation of 1.8. The margin of error at 95% confidence is 1.96 × (1.8 ÷ √400) = 0.18, reported as the interval 7.2 ± 0.18, or (7.02, 7.38). Because n sits under a square root, quadrupling the sample size, not doubling it, is what halves the margin of error.
The formula
Variables
- Critical z-value for the chosen confidence level (e.g. 1.96 for 95%)
- Population standard deviation
- Sample size
The confidence interval is x̄ ± margin of error. A larger n or a lower confidence level reduces the margin of error.
Variables
- Sample proportion
- Sample size
- Critical z-value for the chosen confidence level
Used when estimating a population proportion. The interval p̂ ± ME is widest when p̂ = 0.5.
Check yourself
A consumer agency reports that mean willingness-to-pay for a new product is €38.00 ± €4.00 at 95% confidence, based on 100 respondents. The client asks how to halve the margin of error to ±€2.00 while keeping the same confidence level. Which single change achieves this?