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 $X$.
Pages in category "Examples of Confidence Intervals"
The following 2 pages are in this category, out of 2 total.