Question

Explain the difference between H0 and failing to reject H0. Explain why type 1 error and a Type 2 error have an inverse relationship. Finally given the above think about a situation where you have a test a virus. First you are tested positive or negative.. Second you either really do have the virus or don't . If you actually have the virus but the test did not catch it which error has been made and what is the impact of that error? If you actually don't have the virus but the test says you did, which error is being made and what is the impact of this error ? Which error is the worst one to commit in this situation and why?

Answer 1

The null hypothesis is never accepted. We either reject them or fail to reject them. The distinction between “acceptance” and “failure to reject” is best understood in terms of confidence intervals. Failing to reject a hypothesis means a confidence interval contains a value of “no difference”. However, the data may also be consistent with differences in practical importance. Hence, failing to reject the null hypothesis does not mean that we have shown that there is no difference.

A type I error is known as a false positive while a type II error is commonly referred to as false negative. The errors are inversely related because as one increase, the other decreases.

If you actually have the virus but the test did not catch it then this is a type II error.

If you actually don't have the virus but the test says you did then this is a type I error.

type II is worse as the person with virus will go untreatedfor it in future which may be fatal