Answer to Question #149353 in Statistics and Probability for Jhenny

Question

the probability of type one error cannot be zero

Answer 1

As low as possible is ill defined. You can always make a test with the probability of a Type 1 error 0 but then this test has no power at all. (Think what happens if you take a p-value of 0). You will have to make a trade off between Type 1 and Type 2 errors and what the impact is of each of these errors.