Mathematical Statistics Lecture -

A ( 100(1-\alpha)% ) confidence interval (CI) is a random interval ([L, U]) such that: [ P(\theta \in [L, U]) = 1 - \alpha ] [ \barX \pm z_\alpha/2 \frac\sigma\sqrtn ]

A ( \theta ) is a numerical characteristic of a population distribution (e.g., mean ( \mu ), variance ( \sigma^2 ), success prob ( p )). Parameters are usually unknown ; we use statistics to estimate them. mathematical statistics lecture

The "meat" of most mathematical statistics lectures is . This is where we use sample data to guess unknown values about a population. A ( 100(1-\alpha)% ) confidence interval (CI) is