The correct answer is: A. acceptance of the null hypothesis when it is false and should be rejected.
A type II error is a statistical error that occurs when a researcher fails to reject a false null hypothesis. This means that the researcher concludes that there is no difference between two groups, when in reality there is a difference.
For example, a researcher might be testing the effectiveness of a new drug. The null hypothesis is that the drug does not work. If the researcher fails to reject the null hypothesis, they are concluding that the drug does not work. However, if the drug actually does work, then the researcher has made a type II error.
Type II errors can occur for a number of reasons. One reason is that the sample size is too small. If the sample size is too small, the researcher may not have enough power to detect a difference between the two groups. Another reason for type II errors is that the variability in the data is too high. If the variability is too high, the researcher may not be able to distinguish between a real difference and random variation.
Type II errors can have serious consequences. If a researcher fails to reject a false null hypothesis, they may conclude that there is no difference between two groups when in reality there is a difference. This can lead to the researcher making a decision that is not in the best interests of the participants in the study.
There are a number of ways to reduce the risk of type II errors. One way is to increase the sample size. Another way is to use a more powerful statistical test. Finally, the researcher can try to reduce the variability in the data.
Here is a brief explanation of each option:
- Option A: Acceptance of the null hypothesis when it is false and should be rejected. This is a type II error.
- Option B: Rejection of the null hypothesis when it is true and should be accepted. This is a type I error.
- Option C: Rejection of the null hypothesis when it is false and should be rejected. This is correct.
- Option D: Acceptance of the null hypothesis when it is true and should be accepted. This is a type I error.