Margin of Error and Confidence Intervals

The margin of error tells you how much the sample result might differ from the true population value.

$$\text{Sample result} \pm \text{Margin of error}$$

Example: If a poll finds 52% support with a margin of error of $\pm$3%, the true support is likely between 49% and 55%.

This range is called the confidence interval.

Larger sample size $\to$ smaller margin of error (more precise).

Higher confidence level $\to$ larger margin of error (more certain but less precise).

The approximate formula (for proportions):
$$\text{Margin of error} \approx \frac{1}{\sqrt{n}}$$

where $n$ is the sample size. To halve the margin of error, you need 4 times the sample size!