Error bound

Definition

Error bound in statistics quantifies the maximum expected difference between a sample estimate and the true population parameter. It provides a range within which the true value is expected to lie, given a certain level of confidence.

5 Must Know Facts For Your Next Test

1. The error bound is calculated as $E = z_{\alpha/2} \cdot \sqrt{\frac{p(1-p)}{n}}$, where $z_{\alpha/2}$ is the critical value from the standard normal distribution, $p$ is the sample proportion, and $n$ is the sample size.
2. The error bound decreases as the sample size ($n$) increases.
3. A higher confidence level results in a larger error bound because it requires a wider interval to ensure that it captures the true population parameter.
4. Error bounds are essential for constructing confidence intervals, which provide a range of plausible values for the population proportion.
5. In practical terms, an error bound helps assess the reliability and precision of survey results or experiments.

Review Questions

Related terms

Confidence Interval:

A range of values derived from a sample statistic that is likely to contain the true value of an unknown population parameter.

Sample Proportion:

The ratio of members in a sample with a particular characteristic to the total number of members in that sample.

Critical Value:

A point on the scale of the test statistic beyond which we reject the null hypothesis; often denoted as $z_{\alpha/2}$ in confidence interval calculations.