When can a Type II error occur in hypothesis testing?

A Type II error occurs when the null hypothesis is incorrectly not rejected when it is actually false. This situation reflects a failure in the hypothesis testing process to identify a true effect or difference that exists in the population. In practical terms, it means that the test failed to detect a signal, implying that a conclusion was drawn that there is no significant effect or relationship when, in fact, there is one.

In the context of hypothesis testing, the null hypothesis typically represents a statement of no effect or no difference. Failing to reject the null hypothesis despite the truth that an effect exists can lead to misleading conclusions, especially in fields such as medical research or quality control, where overlooking an important finding can have significant consequences.

The other choices describe different scenarios that do not capture the essence of a Type II error. For example, rejecting the null hypothesis when it is true indicates a Type I error, while having no variability in the sample data or declaring results as not statistically significant does not inherently imply a failure to reject a false null hypothesis. These options do not accurately represent the conditions leading to a Type II error.