The error which occurs by failing to reject a null hypothesis when the alternative hypothesis is true is a Type II error. Type II error is also called false negative because it establishes a false negative evidence for the alternative hypothesis. The probability of occurrence of a Type II error is denoted by beta.
Suppose the null hypothesis is that: Person is not guilty; Type II error indicates that null hypothesis is accepted despite being false i.e a guilty person is set free.
A Type II error may or may not be dangerous when compared to a Type I error- it is dependent on the situation being considered. For example: suppose the null hypothesis is that: person is not healthy; a Type II error would mean that the person is decided as unhealthy – which can be subsequently proved otherwise by carrying out more tests. However, as seen in the earlier example if because of a Type II error, a guilty person is set free it could have dangerous consequences.
Null hypothesis= true
Null hypothesis= false
Reject null hypothesis
Type 1 error
Fail to reject
Type II error
The power of a hypothesis test is given by the probability with which a Type II error will not occur and is given by: