Final answer:
A Type II error occurs when one fails to reject the null hypothesis even though the alternative hypothesis is true. It represents a missed opportunity to identify a real effect or difference in a study. The severity of the consequences depends on the context of the research.
Step-by-step explanation:
Failing to reject the null hypothesis when the research hypothesis is true is known as a Type II error. This is the mistake of not identifying an effect or difference when in fact, one exists. To illustrate, consider if a group of doctors do not proceed with a surgery under the assumption that it would not be beneficial (null hypothesis), but in reality, the surgery could significantly improve patient outcomes (the alternative hypothesis being true). The consequences of a Type II error can be significant, depending on the context.
The probability of a Type II error is denoted by β (beta) and is the complement of the test's power. Hence, if the power of a test is 0.981, the probability of committing a Type II error is 1 - 0.981 = 0.019 or 1.9%. Knowing the power of a test and these probabilities help researchers make informed decisions about their hypotheses.