Margin of Error vs Confidence Level

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.

The confidence level, often 90%, 95%, or 99%, describes the method rather than one specific interval. It says that if you repeated the sampling and interval-building many times, that percentage of the intervals would contain the true parameter. For example, at a 95% confidence level about 95 of every 100 such intervals would trap the real value and about 5 would miss it. A higher confidence level uses a larger critical value, which makes each interval wider.