It does NOT mean there's a 95% probability the true value falls in this specific interval. It means: if you repeated this sampling and interval-construction process many times, about 95% of the resulting intervals would contain the true population value. The confidence describes the reliability of the method, not the probability attached to any one calculated interval.
Should I use a z-interval or a t-interval for a mean?+−
This calculator uses the z-formula, which technically assumes the population standard deviation is known. In practice it's usually estimated from the sample, in which case a t-interval (using the t-distribution instead of the normal distribution) is more accurate, especially for small samples. For large samples (n ≥ 30), the difference between the two becomes small.
Why does a larger sample size narrow the interval?+−
Standard error is proportional to 1/√n, so as sample size grows, the interval narrows — but not proportionally. Quadrupling your sample size only halves the margin of error, which is why sample sizes hit diminishing returns fairly quickly.
What confidence level should I use?+−
95% is the standard default across most fields. Use 99% when the cost of missing the true value is especially high (e.g. safety-critical measurements); 90% is sometimes used for exploratory analysis where a narrower, slightly less certain interval is an acceptable trade-off.