Confidence intervals
Estimation vocabulary: what an interval captures, how wide it is, and what confidence means.
15 terms
Confidence intervalA confidence interval is a range of plausible values for a population parameter, built from a sample as the estimate plus or minus a margin of error.Confidence levelThe confidence level is the long-run percentage of confidence intervals, built the same way from repeated samples, that would capture the true parameter.Coverage probabilityCoverage probability is the rate at which a method's intervals actually capture the parameter, which can fall short of the confidence level they claim.Critical valueA critical value is a cutoff from a reference distribution, such as z or t, that sets a confidence interval's width or a test's rejection boundary.Degrees of freedomDegrees of freedom count the independent pieces of information left after estimation, and they select which t or chi-square curve a statistic follows.Interval estimateAn interval estimate reports a range of plausible values for a parameter, formed as a point estimate plus or minus a margin of error.Margin of errorThe margin of error is the half-width of a confidence interval: a critical value times a standard error, giving the reach on each side of the estimate.Plus-four intervalThe plus-four interval adds two successes and two failures before building a proportion interval, which improves coverage in small samples.PrecisionPrecision is how tightly an estimate pins down a parameter, so a narrower confidence interval is a more precise one.Sample size for a margin of errorThe sample size for a target margin of error is the squared ratio of the critical value to that margin, times p-star times one minus p-star, rounded up.Standard error of a proportionThe standard error of a sample proportion is the square root of p-hat times one minus p-hat, all divided by n.Standard error of the meanThe standard error of the mean is the sample standard deviation divided by the square root of n: how much a sample mean typically varies between samples.T-intervalA t-interval is a confidence interval for a mean that uses a critical value from the t-distribution because the population standard deviation is unknown.Width of a confidence intervalThe width of a confidence interval is the distance from its lower bound to its upper bound, equal to twice the margin of error.Z-intervalA z-interval is a confidence interval whose critical value comes from the standard normal curve, the usual choice for a population proportion.