Financial Risk Manager Part 1

Explanation

In hypothesis testing, the significance level (denoted as α) is defined as the probability of Type I error, which occurs when we reject the null hypothesis (H₀) when it is actually true.

Mathematically: α = P(reject H₀ | H₀ is true)

Given that the test is conducted at the 1% significance level:

• α = 0.01
• Therefore, P(reject H₀ | H₀ is true) = 0.01

Let's analyze the options:

• Option A: P(reject H₀ | H₀ is false) = 0.01 - This describes power (1 - β), not significance level
• Option B: P(reject H₀ | H₀ is true) = 0.01 - CORRECT - This is the definition of significance level
• Option C: P(not reject H₀ | H₀ is false) = 0.01 - This describes Type II error (β)

Key Concepts:

• Significance level (α): Probability of Type I error
• Type I error: Rejecting H₀ when it's true
• Type II error (β): Not rejecting H₀ when it's false
• Power (1 - β): Probability of correctly rejecting H₀ when it's false