Type I Error

Study guide: Exam MAS-I

A Type I Error occurs when a hypothesis test incorrectly rejects a true null hypothesis $H_0$ . It is also called a false positive.

$\alpha = P(\text{Reject } H_0 \mid H_0 \text{ is true})$

$\alpha$ is the significance level of the test, chosen by the analyst before testing (commonly 0.05 or 0.01)
A smaller $\alpha$ makes Type I errors rarer but increases the risk of a Type II Error
The critical region is constructed so that $P(\text{test statistic in critical region} \mid H_0) = \alpha$
In actuarial contexts, a Type I Error might mean incorrectly concluding that a rate change is needed when it is not

Identifying a Type I Error in Ratemaking An actuary tests $H_0$ : the current premium rate is adequate. At $\alpha = 0.05$ , the test rejects $H_0$ and the company increases rates. Later analysis reveals the rates were adequate all along. What type of error occurred?

Answer The null hypothesis was true (rates were adequate) but was rejected. This is a Type I Error. The probability of this occurring was $\alpha = 0.05$ , i.e., there was a 5% chance of this false positive under the testing procedure.