#### Precision and Margin of Error

- In the example, we saw the 95% confidence interval is (0.499,\ 0.901), which is quite big, and therefore is not very useful. There are measures to describe situations like these too.

- The distance between the sample estimate and the endpoints of the confidence interval is called the margin of error (M). For a 95% confidence interval,

M=1.96 \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}

- Therefore, from above, we can see that as n increases, M decreases. This also means that as the sample size increases, the precision of the estimate increase.

- Intuitively, if our random sample is larger, then the random sample should more accurately reflect the population. This also prevents the unintentional bias of selecting samples from a certain subgroup.