Question

Discuss the relationship between the margin of error and the standard error of the mean.

Short answer

The margin of error and the standard error of the mean are directly proportional to each other.

Step-by-step solution

Given Information

Margin of error is represented by $E$.

Standard error of sample mean is represented by$\frac{\sigma }{\sqrt{n}}$.

Explanation

Mathematically, the relationship between the two is represented by

$E=z_{\alpha /2}\times \frac{\sigma }{\sqrt{n}}$

The above relation is true for $100(1-\alpha )\%\mathrm{Cl}$of population mean $\mu$.

Hence, margin of error is product of $z_{a/2}$and standard error of sample mean.

Therefore, margin of error is directly proportional to standard error of the mean.