1. The problem asks which level of significance $\alpha$ to choose if the consequences of making a Type I error are severe. 2. A Type I error occurs when we reject a true null hypothesis. The level of significance $\alpha$ is the probability of making this error. 3. Common significance levels are $0.10$, $0.05$, and $0.01$. A smaller $\alpha$ means a lower chance of making a Type I error. 4. If the consequences of a Type I error are severe, we want to minimize the chance of making that error. 5. Therefore, we choose the smallest significance level, which is $\alpha = 0.01$. Final answer: Choose $\alpha = 0.01$ to reduce the risk of a severe Type I error.