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Confidence Interval for a Mean (t) — result sheet
t-interval for the mean when sigma is unknown.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: df = n - 1; margin = t* x sd/sqrt(n); interval = mean +/- margin.
Uses the t critical value with df bracketing (exact to 30, then 40/60/120, then z). Wider levels and smaller n widen the interval.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Sample mean — Any finite value, same units as data.
- Sample standard deviation — minimum 1.0E-6; maximum 1000000000
- Sample size — minimum 2; maximum 1000000000
- Confidence level — 3 choices
Worked example
| Input | Value |
|---|---|
| Sample mean | 100 |
| Sample standard deviation | 15 |
| Sample size | 16 |
| Confidence level | 95 |
df 15, t* 2.131, margin 7.991; interval (92.009, 107.991).
Assumptions and limits
- Random sample, roughly normal; sigma unknown so t applies.
- Whole-number n >= 2; two-sided interval.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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