Hypothesis Testing with One Sample

A type I error occurs when the null hypothesis $\left(\mathrm{H}_{0}\right)$ is true but is rejected. It is asserting something that is absent, a false hit. A type I error may be compared with a so-called false positive (a result that indicates that a given condition is present when it actually is not present) in tests where a single condition is tested for. A type I error can also be said to occur when we believe a falsehood. In terms of folk tales, an investigator may be "crying wolf" without a wolf in sight (raising a false alarm). $\mathrm{H}_{0}$: no wolf.

The rate of the type I error is called the size of the test and denoted by the Greek letter $\alpha$ (alpha). It usually equals the significance level of a test. In the case of a simple null hypothesis, $\alpha$ is the probability of a type I error. If the null hypothesis is composite, $\alpha$ is the maximum of the possible probabilities of a type I error.