What is a Type II error?

A Type II error occurs when the null hypothesis is not rejected when it is actually false, which is represented by choice C. This means that while there is enough evidence to suggest that the alternative hypothesis is true, the test fails to recognize this and incorrectly maintains the null hypothesis.

Understanding the implications of a Type II error is crucial in hypothesis testing because it suggests that a potentially significant effect or difference has been overlooked. The risk of committing a Type II error is often denoted by the symbol beta (β), and it can be influenced by several factors, such as sample size and the actual effect size. Consequently, researchers aim to minimize the chances of this error, especially in cases where failing to detect an effect could lead to adverse consequences.

In contrast, the other options confound the definitions of Type I and Type II errors. Type I errors are associated with incorrectly rejecting a true null hypothesis, while other choices that refer to accepting the null hypothesis when it is actually true or rejecting the alternative hypothesis do not accurately describe the characteristics of a Type II error. This clarity helps students better grasp the distinctions between the types of errors involved in hypothesis testing.