Category:Examples of Confidence Intervals

This category contains examples of Confidence Interval.

Definition 1

Let $\theta$ be a population parameter of some population.

Let $X$ be a random sample from this population.

Let $I = \openint {\map f X} {\map g X}$ for some real-valued functions $f$, $g$.

$I$ is said to be a $100 \gamma \%$ confidence interval for $\theta$ if:

$\map \Pr {\theta \in I} = \gamma$

where $0 < \gamma < 1$.

Definition 2

Let $X$ be a random variable.

Let $\theta$ be a population parameter of $X$ whose distribution is unknown.

A $100 \paren {1 - \alpha}$ percent confidence interval for $\theta$ is an interval formed by a rule which ensures that, in the long run, $100 \paren {1 - \alpha}$ percent of such intervals will include $\theta$.

This confidence interval is derived from the information obtained from a random sample of observations of $X$.