The two error types differ in which hypothesis is actually true, so a Type I error occurs only when the null is:

1. Each error is defined by pairing a decision with an underlying truth. 2. The decision is to reject the null when the null is true, which is a Type I error. 3. The decision is not to reject the null when, in fact, the null is false, which is a Type II error. 4. So a Type I error is impossible whenever the null is genuinely false. 5. Reducing one error rate generally raises the other. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 9 'Hypothesis Testing with One Sample', sections 9.1-9.6_