When to use it
Use it after checking the population, dependence and estimator assumptions.
A confidence interval is not a probability that this particular realised interval contains the fixed parameter. Small-sample means often require a t method.
Apply it
For a mean with known population standard deviation σ and suitable independent sampling, a normal interval is sample mean ± z* × σ/√n. With estimated σ, use an appropriate t procedure and check assumptions; a prediction interval is a different quantity.
- Specify the parameter and the sampling design.
- Choose an appropriate standard error and critical value.
- Report the interval with its assumptions and practical relevance.
An example in practice
A convenience sample gives a narrow numerical interval but can still be badly biased. Improve recruitment before presenting precision as representativeness.
Source & credit
Standard mathematical statistics; the handbook is an authoritative technical reference, not a claim of sole origin.
NIST/SEMATECH: statistical methods
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