What is a Type II error?

A Type II error occurs when a hypothesis test fails to reject the null hypothesis when it is, in fact, false. In other words, it means that the test does not detect an effect or a difference when one truly exists. This scenario can lead to the incorrect conclusion that there is no effect when there actually is one, which could have significant implications in practical applications such as clinical trials, quality control, or any field where testing hypotheses is crucial.

In this case, the correct answer reflects the definition of a Type II error accurately, emphasizing the failure to recognize that the null hypothesis does not hold true. Understanding this concept is essential for interpreting results from statistical tests and estimating the power of a test, which is the probability of correctly rejecting a false null hypothesis.