Confidence Interval Calculator
以下详细说明暂以英文提供。
How the interval is assembled
A confidence interval wraps the sample mean in the uncertainty of sampling. The standard error, σ ÷ √n, measures how much sample means wobble, and it shrinks with the square root of the sample size — quadruple the data to halve the error. Multiplying by the critical value (1.96 for 95% confidence) turns that wobble into a margin of error, and the interval is mean ± margin. Read the result as a process guarantee: across many samples, about 95% of intervals built this way would capture the true population mean, not that any single interval has a 95% chance of containing it.
常见问题
Why is 95% the usual choice?
It balances precision against caution — wide enough to be trustworthy, tight enough to be useful. Moving to 99% widens the interval by about 31%, while 90% narrows it at the cost of more missed captures.
What if my sample is small?
Below roughly 30 observations, replace the z critical value with the wider t-distribution critical value for n − 1 degrees of freedom, or simply interpret this interval as a slight underestimate of the true uncertainty.