Definition:Confidence Interval/Level

Definition

Let $X$ be a random variable.

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

Consider a $100 \paren {1 - \alpha}$ percent confidence interval for $\theta$.

The confidence level associated with this confidence interval is the coefficient $100 \paren {1 - \alpha}$.

Examples

Common values of confidence levels are:

$90 \%$, corresponding to $\alpha = 0 \cdotp 10$

$95 \%$, corresponding to $\alpha = 0 \cdotp 05$

$99 \%$, corresponding to $\alpha = 0 \cdotp 01$

$99 \cdotp 9 \%$, corresponding to $\alpha = 0 \cdotp 001$

Also see

• Results about confidence intervals can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): confidence level
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): confidence level