Researchers conducting a study with ____ power have a _____ probability of committing a type ____ error.

In hypothesis testing, the power of a statistical test refers to the probability that the test correctly rejects a false null hypothesis. When researchers are dealing with low power, this implies that there is a limited ability to detect an effect if one truly exists. Consequently, with low power, the chances of making a type II error, which occurs when a researcher fails to reject a false null hypothesis, increase significantly.

Hence, researchers conducting a study with low power inherently have a high probability of committing a type II error. This understanding is rooted in the relationship between power, the likelihood of detecting true effects, and the misclassification that occurs when true positives are overlooked due to insufficient study sensitivity.

In contrast, with high power, researchers would have a low probability of making a type II error, indicating a stronger ability to detect effects when they are present. This conceptual framework is essential for evaluating the effectiveness and reliability of a study's findings.