Which of the following is an accurate definition of a Type II error?

a. rejecting a false null hypothesis
b. rejecting a true null hypothesis
c. failing to reject a false null hypothesis
d. failing to reject a true null hypothesis

http://www.investopedia.com/terms/t/type-ii-error.asp

The accurate definition of a Type II error is option C: failing to reject a false null hypothesis.

To understand why this definition is correct, let's break it down. In hypothesis testing, we are trying to make a decision about a population based on a sample of data. We start by assuming a null hypothesis (H0) that there is no significant difference or relationship in the population. The alternative hypothesis (H1 or Ha) states that there is a significant difference or relationship.

In the context of Type II error, we are specifically considering situations where the null hypothesis is false (H0 is actually incorrect, and there is a significant difference or relationship). In such cases, it would be desirable to reject the null hypothesis and conclude that there is indeed a significant difference or relationship (which is the goal of hypothesis testing).

However, sometimes our sample data may not provide strong enough evidence to reject the null hypothesis, even though it is actually false. This is known as a Type II error – we inaccurately fail to reject the false null hypothesis.

An example can further illustrate this concept: Suppose we are testing a new drug and want to determine if it is effective in treating a certain condition. The null hypothesis (H0) would state that the drug has no effect, while the alternative hypothesis (H1 or Ha) would state that the drug has an effect.

If we conduct a study and find that the data does not provide enough evidence to reject the null hypothesis (H0), even though the drug does have an effect, then we have committed a Type II error. We have failed to reject a false null hypothesis.

In summary, a Type II error occurs when we mistakenly fail to reject a false null hypothesis, meaning that we do not detect a significant difference or relationship in the sample data, despite the existence of one in the population.

The accurate definition of a Type II error is:

c. failing to reject a false null hypothesis