A type II error (also referred to as a false negative) is when a hypothesis test fails to reject the null hypothesis, even though it should have been rejected based on the true population value. It occurs when the null hypothesis is found to be true, but it is not the case for the entire population. A type II error essentially represents a missed opportunity for a researcher to learn the true state of the population.

In the context of hypothesis testing, the type II error rate is determined by the probability of incorrectly failing to reject the null hypothesis. This rate is influenced by three main factors: the sample size, the true population size, and the pre-set alpha level. Analysts must consider the magnitude of the risk of a type II error when evaluating the probability of a type I error.

The sample size is an important factor for lowering the risk of a type II error. A larger sample size offers more data to make decisions on, thereby reducing the likelihood of a false negative. The true population size is another contributing factor to the potential risk of a type II error. If the population size is larger, then the risk of a false negative increases. Finally, the pre-set alpha level also affects the magnitude of risk of a type II error. A smaller alpha level leads to more stringent criteria for rejecting the null hypothesis, making it less likely to incorrectly fail to reject the null when it should be rejected. However, this also increases the chances of a false positive.

In short, a type II error occurs when a hypothesis test erroneously fails to reject a false null hypothesis. The risk of a type II error can be minimized by careful consideration of the sample size, true population size, and alpha level. Analyst must weigh the risk of a type II error with the risk of a type I error to properly evaluate hypothesis testing results.