FAQs
1) When should I use t instead of z?
Use t when population σ is unknown and you estimate variability using the sample SD. It matters most for small samples, because t has heavier tails and yields wider intervals.
2) What does a 95% confidence interval mean?
If you repeated the same sampling process many times, about 95% of the constructed intervals would contain the true population mean. It does not mean the mean has a 95% probability of being inside one specific interval.
3) Can I paste data with new lines or commas?
Yes. The calculator accepts commas, spaces, semicolons, and new lines. It ignores non-numeric items, so keep the input mostly numbers for best results.
4) Why does the interval widen when confidence increases?
Higher confidence requires a larger critical value, which increases the margin of error. You trade precision for assurance that the interval will capture the true mean more often.
5) What if my data are skewed or have outliers?
Outliers inflate the SD and widen the interval, while strong skew can make normal-based intervals less reliable for small n. Consider transformations, robust estimators, or bootstrap intervals when distribution issues are severe.
6) What is the difference between sample SD and population SD?
Population SD describes the entire population and is rarely known. Sample SD estimates it from data; using n−1 corrects bias in the variance estimate and is standard for inference.
7) How accurate are the critical values here?
z uses a high-accuracy inverse normal approximation. t uses a well-known expansion based on z and degrees of freedom; accuracy is strong for practical CI work and improves as df grows.
8) Can I export and share my results?
Yes. After you submit, use the download buttons to export a CSV or a one-page PDF summary. The export uses your most recent calculation stored for this browser session.