The kind of errors that are possible in the hypothesis-testing process. The kind of errors we consider here are about how, in spite of doing all your figuring correctly, you consider here are about how, in spite of doing all your figuring correctly, your conclusion from hypothesis-testing can still be incorrect. It is not about making mistakes in calculations or even about using the wrong procedures. That is, mistakes in calculations or even about using the wrong procedures. That is, decision errors are situations in which the right procedures lead to the wrong decisions.
Decision errors are possible in hypothesis testing because you are making decisions about populations based on information in samples. The whole hypothesis testing process is based on probabilities. The hypothesis-testing process is set up to make the probability of decision errors as small as possible. For example, we only decide to reject the null hypothesis if a sample’s mean is so extreme that there is a very small probability (say, less than 5%) that we could have gotten such an extreme sample if the null hypothesis is true. But a very small probability is not the same as a zero probability! Thus, in spite of your best intentions, decision errors are always II errors.