The margin of error is the distance from a confidence interval's midpoint to either endpoint. For Juniper's supplied one-sample mean method:
[ MOE=t^*(s/\sqrt{n}). ]
Compute with full precision, then check that the lower and upper endpoints are equally distant from the sample mean. Rounding the standard deviation or standard error too early can make that reconciliation fail.
What narrows the interval
- A larger sample size reduces the simple standard error through (\sqrt{n}).
- Lower observed spread reduces (s).
- A lower confidence level generally uses a smaller critical value.
Each change has a consequence. More observations cost time or money; lower confidence means lower long-run coverage; and lower sample spread may be an accident of the selected units. An analyst should not trim valid tail values to manufacture a smaller margin.
The margin describes sampling precision under the method. It is not a general allowance for every error in the source, model, accounting estimate, valuation, forecast, or decision.
Put the concept to work
Understand this concept
- Explain how critical value, estimated standard error, sample spread, and sample size drive interval half-width while leaving nonsampling error outside it.
Apply this concept
- Compute a supplied-critical-value margin of error, reproduce both interval endpoints, and reconcile the midpoint and half-width at full precision.
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Build on these ideas
- Confidence interval — Understand
To understand this concept: Required. The half-width has meaning only within a declared interval procedure.
- Margin of error — Understand
To apply this concept: Required. Reconciliation applies the interval half-width identity.
- Standard error — Understand
To understand this concept: Required. The margin multiplies a critical value by the estimate's standard error.
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- Margin of error — Apply
Required level here: understand. Required. Reconciliation applies the interval half-width identity.