# type II error calculation

• July 8th 2010, 07:50 AM
statsvenu
type II error calculation
Hi

Any Body pass me the formula for Type II error in testing of Hypothesis

REgards
Statsvenu
• July 8th 2010, 03:45 PM
Danneedshelp
A type II error occurs when one fails to reject the null hypothesis when the alternative is indeed true. The probability of a type II error is denoted by $\beta$. Conisder the following test:

$H_{0}:\theta=\theta_{0}$ vs. $H_{a}:\theta=\theta_{a}$

Then, by the definition above, the probability of a type II error, $\beta$ is

$\beta=P(\theta$ is not in the rejection region when $\theta=\theta_{a})$.

Notice, this is a simple hypothesis test. We can only compute a type II probability for specific values of $\theta_{a}$.