Final answer:
In hypothesis testing, the power of a test is the probability of correctly rejecting the null hypothesis, represented as 1 – β, with β being the probability of a Type II error(option b). The power of a test is different from the level of significance (α), which is the risk of a Type I error.
Step-by-step explanation:
When testing a hypothesis, the power of a test is best described as the b) probability of correctly rejecting the null hypothesis.
This is opposite to a Type I error (level of significance), which is the probability of erroneously rejecting a true null hypothesis. The power of the test is denoted as 1 – β, where β represents the probability of making a Type II error, meaning the error of failing to reject the null hypothesis when it is actually false. Therefore, a high power is desirable and indicates a high chance of detecting a true effect when it exists. To improve the power of the test, researchers might increase the sample size while maintaining the same preset α (significance level).
It's important to note that α and β are distinct concepts in hypothesis testing: α is the preset level of significance, often set at 0.05, while β is tied to the power of a test and is used for determining the appropriate sample size. By setting a low significance level, one minimizes the chance of a Type I error; however, ensuring a low β will increase the power and reduce the risk of a Type II error.