The risk of failing to reject the Null Hypothesis when in fact the Alternative Hypothesis is true. The probability of a Type II Error is denoted by the Greek letter Beta. It is considered tobe the lesser error of the two Errors. In terms of the criminal court situation, it is the chance of acquitting a guilty person.
The power of the test is calculated as (1- Beta). It gives the probability of rejecting the null hypothesis when the alternative is in fact true, a correct decision. In terms of the criminal court, it is the chance of convicting the defendent when the defendent is actually guilty.
Ideally, we want to eliminate or at least minimize the chances of both types of errors to maximize the chance of making the right decision. Unfortunately, it is not possible to minimize both errors simultaneously, since reducing one leads to an increase in the other. We try to overcome this problem by setting alpha (the more serious error) at an acceptable level (usually 0.05, or 5%) and then minimizing beta for the fixed alpha value.
Type I and Type II Errors on Hyperstat Onlineby David M. Lane - http://davidmlane.com/hyperstat/A18652.html