Making false positive and false negative errors

Question

In the Ted Talk video (Donnelly 2005), he gives us examples of jury decisions and medical tests related to making false positive and false negative errors. His video connects to what I have learned in this curriculum surrounding statistical decision making by demonstrating how easy it can be to make Type I or II errors. Donnelly cited a hypothetical example of a false positive or type 1 error for medicine. He illustrated that if a person were picked at random to test for HIV and they have a positive result, we might reject the null hypothesis that the individual does not
have the disease and make a type 1 error. One consequence of making this Type 1 error might be that the individual suffers unnecessary stress by believing that they have HIV when they actually do not.