Q 8.43 - Elementary Statistics

Question

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

Step-by-Step Solution

Answer

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

Step 1: Given Information

Margin of error is represented by $E$.

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

Step 2: 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.