Financial Risk Manager Part 1

The p-value is defined as the smallest level of significance at which the null hypothesis (H₀) can be rejected. It represents the probability, assuming H₀ is true, of observing a test statistic at least as extreme as the value observed.

Key points:

• Option A & B are incorrect because they state "highest level" rather than "lowest level"
• Option C is correct: p-value is the lowest significance level at which H₀ can be rejected
• Option D is incorrect: This describes the probability of Type II error (accepting H₀ when it is false), not the p-value

Understanding p-value:

• If p-value ≤ α (significance level), reject H₀
• If p-value > α, fail to reject H₀
• Smaller p-values provide stronger evidence against H₀

Example: If p-value = 0.03, this means H₀ can be rejected at any significance level α ≥ 0.03, and 0.03 is the smallest such level.