The correct answer is:

d. The probability of incorrectly rejecting a true null hypothesis.

Explanation:

The significance level, often denoted by α (alpha), is the threshold at which we reject the null hypothesis. It is defined as the probability of making a Type I error, which occurs when the null hypothesis is true but is incorrectly rejected. The significance level is commonly set at 0.05, meaning there is a 5% chance of rejecting the null hypothesis when it is actually true.

• a. refers to the probability of accepting the alternative hypothesis, which is not what the significance level represents.
• b. confuses significance level with the p-value, which is the probability of obtaining results as extreme as the ones observed, assuming the null hypothesis is true.
• c. refers to the probability of accepting a true null hypothesis, which is the confidence level (1 - α), not the significance level.
• e. refers to a Type II error, which occurs when the null hypothesis is not rejected when it is false. This is unrelated to the significance level.

Do you want further clarification or examples?

Here are some related questions to expand your knowledge:

1. What is the difference between a Type I and a Type II error?
2. How is the p-value related to the significance level?
3. What happens if we lower the significance level to 0.01 instead of 0.05?
4. How do we choose the significance level in different types of tests (e.g., one-tailed vs two-tailed)?
5. What is the confidence level in hypothesis testing, and how is it related to the significance level?

Tip: Lowering the significance level reduces the chance of a Type I error, but it increases the risk of a Type II error. You need to balance the two based on the consequences of each type of error in your context.