Financial Risk Manager Part 1

Explanation

The level of significance (α) in hypothesis testing represents the probability of making a Type I error - rejecting the null hypothesis when it is actually true.

Key concepts:

• Type I error (α): Rejecting H₀ when H₀ is true (false positive)
• Type II error (β): Failing to reject H₀ when H₀ is false (false negative)
• Power (1-β): Probability of correctly rejecting H₀ when it is false

When α decreases:

1. Type I error probability decreases: Since α directly represents the probability of Type I error, decreasing α reduces the chance of rejecting a true null hypothesis.
2. Type II error probability increases: There's a trade-off - making the test more conservative (lower α) makes it harder to reject H₀, which increases the chance of failing to reject a false null hypothesis.
3. Power decreases: With lower α, the test becomes less powerful (less likely to detect true effects).

Why option C is correct: Option C states: "The likelihood of rejecting the null hypothesis when it's in fact true decreases" - This is exactly the definition of Type I error, and since α represents this probability, decreasing α directly reduces this likelihood.

Why other options are incorrect:

• A: Incorrect - Decreasing α actually increases the likelihood of Type II error
• B: Incorrect - Decreasing α decreases, not increases, Type I error probability
• D: Incorrect - This is contradictory; decreasing α reduces, not increases, Type I error frequency

Practical example: If α = 0.05, we're willing to accept a 5% chance of false rejection. If we decrease to α = 0.01, we're only willing to accept a 1% chance of false rejection, making the test more conservative.