Step 1 :If the consequences of making a Type I error are severe, we would want to minimize the probability of making such an error. This is done by choosing a smaller level of significance, \(\alpha\). The level of significance is the probability of rejecting the null hypothesis when it is true, which is a Type I error. Therefore, we would choose \(\alpha = 0.01\) to minimize the probability of a Type I error.
Step 2 :Final Answer: \(\boxed{0.01}\)