
Answer-first summary for fast verification
Answer: P(reject H₀ | H₀ is true) = 0.01
## 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
Author: Tanishq Prabhu
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