Margin of error and confidence intervals

What the margin of error is

• Because of sampling variability, a poll's result is an estimate, not the exact truth. The margin of error (MoE) says how far the estimate could reasonably be from the true value.
• For a percentage from a random sample of size $n$, a useful approximate 95% margin of error is:

$\text{MoE} \approx \frac{1}{\sqrt{n}}$

• This is a percentage (as a decimal), so multiply by 100 to express it in percentage points.

Confidence intervals

• A confidence interval is the estimate give or take the margin of error:

$\text{estimate} \pm \text{MoE}$

• A 95% confidence interval means: if the survey were repeated many times, about 95% of such intervals would contain the true population value.

How sample size affects the margin

• The margin of error shrinks as $n$ grows, but slowly (it depends on $\sqrt{n}$).
• To halve the margin of error you need four times the sample size.