Given the following null hypothesis, give an example of a Type II error.
H0: There is no difference in the level of understanding of this chapter between students who have previously taken a statistics course and students who have not previously taken a statistics course.
Accepting Ho when it is actually false.
To understand Type II error in the context of the given null hypothesis, it is important to first understand the two types of errors in hypothesis testing:
1. Type I error (α error): This occurs when you reject a true null hypothesis. In other words, you conclude that there is an effect or difference when, in reality, there is none.
2. Type II error (β error): This occurs when you fail to reject a false null hypothesis. It means that you conclude there is no effect or difference when, in fact, there is one.
In the given null hypothesis, we are testing if there is no difference in the level of understanding between students who have previously taken a statistics course and students who have not.
An example of a Type II error in this scenario would be if, based on the statistical analysis, we fail to reject the null hypothesis and conclude that there is no difference in the level of understanding. However, in reality, there actually is a difference in the understanding between the two groups. This means that we have made a Type II error by failing to detect the difference that does exist.
In simpler terms, a Type II error occurs when we fail to detect a real effect or difference in the data due to insufficient sample size, inadequate statistical power, or other factors that lead to a false conclusion of no difference.