Read an interval as a procedure

The idea

An estimate summarizes a sample, while an interval expresses uncertainty under a statistical model. An interval is useful because many different samples could have been observed. Its interpretation depends on the sampling process, assumptions, and method used to construct it.

Worked example

A repair cooperative samples service times and estimates an average of 40 minutes, with a model-based interval from 36 to 44. The manager avoids promising that every repair will take under 44 minutes: the interval concerns a mean, not individual durations. She also checks whether weekend emergency repairs were excluded. A narrow interval from only easy weekday work could mislead scheduling even if its arithmetic were flawless.

Use it carefully

For a conventional 95% confidence procedure, the coverage statement concerns its long-run performance over repeated samples under the model. It is not a promise that 95% of individual observations fall inside the reported interval. Precision cannot rescue unrepresentative data. When communicating the result, name the quantity, population, period, and method, then discuss practical variation separately.

RETRIEVE. REASON. REMEMBER.

Knowledge check.

Choose one answer for each question, then check your reasoning.