Answer: Both statements are incorrect.

## Explanation Let's analyze each statement: **Statement I:** "Decreasing the significance level will decrease the probability of failing to reject a false null" - The significance level (α) is the probability of rejecting the null hypothesis when it is true (Type I error). - Decreasing α makes it harder to reject the null hypothesis. - The probability of failing to reject a false null hypothesis is β (Type II error). - When α decreases, β increases because we're being more conservative about rejecting the null. - Therefore, decreasing the significance level will **increase** (not decrease) the probability of failing to reject a false null. **Statement II:** "Decreasing the significance level will increase the power of the test" - Power of a test = 1 - β = Probability of correctly rejecting a false null hypothesis. - When α decreases, β increases (as explained above). - If β increases, then power (1 - β) decreases. - Therefore, decreasing the significance level will **decrease** (not increase) the power of the test. **Conclusion:** Both statements are incorrect. **Key Relationships:** - α (significance level) = P(Type I error) - β = P(Type II error) = P(failing to reject a false null) - Power = 1 - β - When α decreases → β increases → Power decreases

Author: Nikitesh Somanthe