Confidence Interval vs Margin of Error

A confidence interval gives a range for an unknown population parameter instead of a single guess, acknowledging that samples vary. Its width reflects the uncertainty in the estimate: more data and less spread give a narrower interval. For example, a 95% confidence interval of 52% plus or minus 3% for support runs from 49% to 55%. The general form is $\text{estimate} \pm (\text{critical value}) \times (\text{standard error})$, where the standard error measures the typical size of sampling error.

The margin of error sets the reach on each side of a point estimate in a confidence interval, so the interval is $\text{estimate} \pm \text{margin of error}$. It grows with the confidence level and shrinks as the sample size grows, since more data lower the standard error. For example, a poll reporting 47% with a 3% margin of error gives the interval 44% to 50%. In symbols, $\text{margin of error} = z^* \cdot \frac{\sigma}{\sqrt{n}}$ for a mean with known population standard deviation $\sigma$, where $z^*$ is the critical value and $n$ the sample size.