Confidence levels widen around one fixed sample meanUpdates with every input
Math & Statistics
Confidence Interval Value Table Calculator
Generate a live confidence-interval value table for one sample mean across several confidence levels, with nested endpoints, critical values, widths, and benchmark coverage shown without recomputing the sample statistics.
Standard error -
Degrees of freedom -
Narrowest interval -
Widest interval -
Width expansion -
First level covering benchmark -
Shared center -
Intervals generated -
NESTED INTERVAL FAN
Confidence levels widen around one fixed sample mean
Every rail shares one center and standard error, making the price of greater confidence visible as symmetric endpoint expansion.
CRITICAL VALUE REGISTER
Exact endpoint table for the selected confidence ladder
The live table is the reusable value reference: confidence, t critical, margin, endpoints, width, and benchmark coverage.
| Confidence | t critical | Margin | Lower | Upper | Width | Benchmark |
|---|
TABLE DESIGN
Use one sample and one stated family of confidence levels
- Enter the sample mean, SD, and n once.
- Choose the lowest and highest confidence levels needed for reporting.
- Use a modest row count so adjacent levels remain distinguishable.
- Enter a benchmark only if it has a substantive interpretation.
- Copy the exact row whose confidence level matches the reporting protocol.
WIDTH TRADEOFF
More confidence means less precision for the same data
All intervals in the fan use the same observations. Higher confidence increases the critical value and therefore the margin of error.
Selecting a confidence level after examining which row includes a preferred benchmark is data-dependent reporting and should be avoided.
VALUE-TABLE ENGINE
Hold the data fixed and vary only the confidence level
One standard error is calculated from the entered sample. Each row changes only the two-sided t critical value, so widening can be attributed to confidence rather than to altered data.
Detailed calculation process and general formulas
SE = s / sqrt(n)alpha = 1 - Ct* = t_(1-alpha/2, n-1)ME_C = t* x SECI_C = mean +/- ME_CSymbols, meanings, and units
- C
- row confidence levelproportion
- alpha
- two-tail probability outside the intervalproportion
- SE
- standard error shared by all rowsoutcome units
- t*
- row-specific t critical valueunitless
- CI_C
- interval at confidence Coutcome units
TABLE USES
A value table is useful when the decision protocol is not yet frozen
The ladder exposes consequences without pretending every row is a separate analysis.
Protocol comparison
-Compare widths before the confidence level is chosen by policy.
Benchmark visibility
-See the first listed level whose interval contains the benchmark.
Reproducible reporting
The table preserves critical values and endpoints for audit or teaching.
Decision takeaway: Choose the confidence level by the reporting objective, not by the desired conclusion.
Applied decisions
When an interval ladder adds clarity
Engineering report options
A team compares 90%, 95%, and 99% interval widths before fixing its reporting standard.
What the result clarifies: The fan shows the precision cost of the stricter coverage target.
Statistics instruction
Students hold mean, SD, and n fixed while changing confidence.
What the result clarifies: Only the critical value and endpoints move.
Worked current scenario
Substitution, intermediate values, and reconciliation
Method references
Sources for this calculator's specific method
Scope and limitations
The table does not create additional evidence by displaying more confidence levels. Every row relies on the same sample and assumptions. Do not cherry-pick a row after inspecting benchmark coverage.
Confidence Interval Value Table Calculator | Confidence-Level Ladder FAQ
Why is the center identical in every row?
Changing confidence affects the critical value and margin, not the sample mean.
Are the intervals independent?
No. They are nested calculations from the same sample.
Can I use z critical values?
This calculator intentionally uses Student t critical values because the population SD is not assumed known.