What does it mean if a test has a power of 0.80?

A test having a power of 0.80 means that it has an 80% probability of correctly identifying a true effect when one exists, which aligns with the correct answer. This is a key concept in hypothesis testing, as power is a measure of a test's ability to detect an effect when it is truly present. Higher power reduces the risk of a Type II error, or failing to reject a false null hypothesis.

In contrast, the other options do not accurately define what a power of 0.80 indicates. While rejecting null hypotheses is a part of hypothesis testing, saying the test correctly rejects 80% of them doesn't precisely capture the notion of power, which specifically pertains to true positives rather than just rejections. The likelihood of a Type I error refers to the probability of incorrectly rejecting a true null hypothesis and is typically set by the alpha level, not related to the test's power. Lastly, being significant at the 0.80 alpha level pertains to the criteria for rejecting the null hypothesis, not the power of the test itself. Thus, option C is the most accurate representation of what having a power of 0.80 means.