Error bound for a population mean

Definition

The error bound for a population mean is the maximum expected difference between the true population mean and a sample estimate of that mean. It is often referred to as the margin of error in confidence intervals.

5 Must Know Facts For Your Next Test

1. The error bound for a population mean depends on the standard deviation of the population, the sample size, and the confidence level.
2. For normally distributed populations with known standard deviations, the Z-distribution is used to calculate the error bound.
3. When the population standard deviation is unknown and sample size is small, the Student's t-distribution is used instead.
4. A larger sample size results in a smaller error bound, increasing the precision of your estimate.
5. The formula for calculating error bound using the Z-distribution is $E = Z_{\alpha/2} \cdot \frac{\sigma}{\sqrt{n}}$ and using t-distribution is $E = t_{\alpha/2} \cdot \frac{s}{\sqrt{n}}$.

Review Questions

• What factors influence the magnitude of the error bound for a population mean?
• How does increasing sample size affect the error bound?
• What distributions are used to calculate error bounds when standard deviation is known vs. unknown?

Related terms

Confidence Interval:

A range of values derived from a sample that is likely to contain the true population parameter with a specified level of confidence.

Margin of Error:

Another term for error bound; it quantifies uncertainty around an estimate from a sample.

Standard Error:

An estimate of the standard deviation of a sampling distribution; it measures how much variability exists in an estimate.