Final answer:
The correct answer is B: The power of a statistical test is its ability to detect real differences between population means. High power means a lower chance of a Type II error and a better ability to detect actual effects.
Step-by-step explanation:
The power of a statistical test is its ability to detect real differences between population means. This is referred to as the test's power, and it is formally defined as 1 minus the probability of making a Type II error (also known as β error), which occurs when a test fails to reject a false null hypothesis. Consequently, a test with high power will have a lower chance of committing a Type II error, meaning it is more likely to detect an actual effect or difference when one exists.
Inferential statistics interpret data to test hypotheses through various methods, such as t-tests, to compare means or to assess differences between groups. It is important for these tests to have high power to ensure that actual differences are not overlooked. One common way to increase a test's power is by increasing the sample size, which can help improve the likelihood of detecting real effects.
To summarize, Option B from the initial question is correct: The power of a statistical test is its ability to detect real differences between population means. This is a crucial aspect of hypothesis testing, as statisticians aim to draw appropriate conclusions from the data collected.