Answer: The likelihood of rejecting the null hypothesis when it's in fact true decreases

## 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.

Author: Nikitesh Somanthe