Visualize exactly what the "Margin of Error" means geometrically on a normal curve.
Observe how increasing the Sample Size ($n$) shrinks the Margin of Error.
Observe how demanding higher Confidence ($C\%$) dramatically widens the Margin of Error.
Key Mathematical Formula
$ME$ = $Z^* \times \frac{\sigma}{\sqrt{n}}$
Because $\sqrt{n}$ is exclusively in the denominator, quadrupling $n$ only cuts the error in half. Meanwhile $Z^*$ grows non-linearly with confidence demands.
Tags
StatisticsInferenceMargin of ErrorConfidence
Interval vs True Parameter (Mean)
Margin of Error ($ME$)0.00
Width of Interval0.00
Confidence Level ($C\%$) 95%
Critical Value $Z^*$ = 1.96
Sample Size ($n$) 100
Try this: Set Confidence to 99%. Look how wide the interval gets. To shrink the interval back down without dropping confidence, you MUST drag the sample size $n$ substantially higher.
Quick Quiz
You want to cut the margin of error EXACTLY in half. What must you do to your sample size?