The calculation, without hidden assumptions
Confidence intervals quantify sampling uncertainty around an estimate. MAXScanner separates three common models instead of hiding them behind one formula: a z interval when population σ is genuinely known, a t interval when σ is estimated by the sample SD, and a Wilson interval for a binomial proportion. The result shows the standard error, critical value and margin of error or Wilson bounds.
How to use this calculator
Choose the statistical model that matches the data and what is known.
Enter the summary values and select 90%, 95% or 99% confidence.
Review the interval, standard error/critical value and method note before reporting the result.
Where people use it
- •Reporting uncertainty around sample means
- •Textbook and analysis checks for t versus z intervals
- •Confidence intervals for observed proportions
Example: mean 72, sample SD 15, n = 25 at 95%
With σ unknown, the calculator uses a t critical value with 24 degrees of freedom, not z = 1.96. The wider t interval reflects the extra uncertainty from estimating σ.
What the result does not assume
- •A confidence level describes the long-run coverage of the interval-building procedure, not the probability that a fixed computed interval contains the parameter.
- •The formulas assume the sample/design conditions for the selected method are reasonable. Dependence, severe bias or inappropriate sampling cannot be repaired by the calculator.
- •The t critical values are standard two-sided values for 90%, 95% and 99% confidence.
Frequently asked questions
When should I use t instead of z for a mean?+
Use t when the population standard deviation is unknown and the sample standard deviation is used in its place. The degrees of freedom are n−1.
Why use Wilson for a proportion?+
Wilson intervals generally behave better than the simple Wald p̂ ± z√(p̂(1−p̂)/n), especially with smaller samples or proportions near 0 or 1.
Does a 95% interval have a 95% chance to contain the true value?+
Under the frequentist interpretation, the parameter is fixed. The 95% refers to the long-run success rate of the method over repeated samples.
Semantic next steps
Continue the calculation
These links move to a different input, formula or project stage rather than a keyword variation of this page.
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MAXScanner keeps the formula and assumptions beside the result so you can verify the number before using it in a drawing, estimate, specification, worksheet or document. Where a supplier, manufacturer, drawing or applicable standard owns a requirement, that source remains authoritative.