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

• What happens to the error bound when you increase the sample size?
• How does changing the confidence level affect the error bound?
• Why is it important to calculate an error bound when estimating a population proportion?

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.