A range computed from a sample by a method that, over repeated samples, captures the true parameter a stated share of the time, such as 95%. The 95% describes the method, not the chance that this particular interval contains the true value.
Card 1 of 244. Answer: A range computed from a sample by a method that, over repeated samples, captures the true parameter a stated share of the time, such as 95%. The 95% describes the method, not the chance that this particular interval contains the true value.
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A confidence interval gives a plausible range for a parameter such as a mean, together with a confidence level. For a mean it is usually x̄ ± t* × s/√n: the sample mean plus or minus a critical value times the standard error. Higher confidence means a wider interval, and more data means a narrower one, shrinking with √n.
Example: 100 delivery times have a mean of 32 minutes and a standard deviation of 10. The standard error is 10/√100 = 1, and the t critical value for 99 degrees of freedom is 1.98, so the 95% interval runs from about 30.0 to 34.0 minutes. Halving its width takes four times as many deliveries.
The classic trap: once computed, the interval either contains the true mean or it doesn't. The 95% is the long-run hit rate of the procedure; a Bayesian credible interval is what gives a probability for the parameter itself. Two more follow-ups: a 95% interval for a difference that excludes zero matches p < 0.05 in a two-sided test, and an interval for the mean is not a range for individual values. That is a prediction interval, which is much wider.
