Texas A&M University (TAMU) MATH140 Mathematics for Business and Social Sciences Final Practice Exam

In hypothesis testing, a type I error occurs when a true null hypothesis is incorrectly rejected. This means that the test indicates that there is an effect or a difference when, in fact, there is none. This type of error is often referred to as a "false positive," and its significance level is denoted by alpha (α), which represents the probability of making this type of error.

Choosing the correct answer reflects an understanding of the fundamental concepts of hypothesis testing. When we set up a hypothesis test, we begin with a null hypothesis, which represents a default position or a claim of no effect or no difference. If we reject this null hypothesis based on sample evidence, we are making a claim that there is sufficient evidence to support an alternative hypothesis. If we do so while the null hypothesis is actually true, that is a type I error.

To clarify, a type II error occurs when a false null hypothesis is not rejected, implying a failure to identify an effect or a difference that does exist; it is known as a "false negative." This highlights the distinction between the two types of errors—type I involves rejecting a true null hypothesis, while type II involves failing to reject a false one.

Understanding these errors is crucial in making informed decisions based