What is a Type II error?
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A. B. C. D. E.B
The type II error is accepting the null hypothesis when it is actually false.
A Type II error, also known as a false negative, occurs when we fail to reject a null hypothesis that is actually false. In other words, it's the incorrect acceptance of a false null hypothesis. To understand Type II error, let's break down the components of hypothesis testing:
Null hypothesis (H₀): It represents the status quo or the assumption that there is no significant difference or relationship between variables. It assumes that any observed difference or relationship is due to chance.
Alternative hypothesis (Hₐ or H₁): It contradicts the null hypothesis and suggests that there is a significant difference or relationship between variables. It represents the researcher's claim or the hypothesis they aim to support.
During hypothesis testing, we collect and analyze data to make a decision about the null hypothesis. The two possible decisions are:
Reject the null hypothesis (H₀): This decision implies that there is sufficient evidence to support the alternative hypothesis (Hₐ). It suggests that the observed difference or relationship between variables is not due to chance alone.
Fail to reject the null hypothesis (H₀): This decision implies that there is insufficient evidence to support the alternative hypothesis (Hₐ). It suggests that the observed difference or relationship between variables could be due to chance.
Now, let's relate these decisions to Type II error:
A Type II error occurs when we fail to reject the null hypothesis (H₀) when it is actually false. In other words, we fail to detect a significant difference or relationship between variables, even though one exists in reality.
In the given answer choices:
A. Rejecting a false alternative hypothesis: This does not represent Type II error because rejecting a false alternative hypothesis would actually be the correct decision.
B. Accepting a false null hypothesis: This is the correct definition of Type II error. Accepting a false null hypothesis means we fail to reject the null hypothesis when it is false.
C. None of these answers: This is incorrect because Type II error is defined by accepting a false null hypothesis.
D. Accepting a false alternative hypothesis: This does not represent Type II error because accepting a false alternative hypothesis would be an incorrect decision.
E. Rejecting a false null hypothesis: This represents the correct decision, not a Type II error. Rejecting a false null hypothesis means we correctly reject the null hypothesis when it is false.
Therefore, the correct answer is B. Accepting a false null hypothesis.