If the chosen significance level is $\alpha$ = $0.05$, then there is a 5% chance of which of the following?

• A. Failing to reject the null hypothesis when it is actually false (Type II error)
• B. Selecting a sample with a mean equal to the population mean
• C. Rejecting the null hypothesis when it is actually true (Type I error)
• D. Obtaining a p-value greater than $0.05$

Answer: (C)

Verified step by step guidance

1. Understand that the significance level \( \alpha \) represents the probability of making a Type I error in hypothesis testing.
2. Recall that a Type I error occurs when we reject the null hypothesis \( H_0 \) even though it is actually true.
3. Recognize that setting \( \alpha = 0.05 \) means we accept a 5% risk of incorrectly rejecting \( H_0 \) when it is true.
4. Note that a Type II error, failing to reject \( H_0 \) when it is false, is related to \( \beta \), not \( \alpha \).
5. Therefore, the 5% chance associated with \( \alpha = 0.05 \) specifically refers to the probability of making a Type I error.