Below is a question on a recent actuarial exam, Exam 3L of the CAS. I didn't know whether or not to use the continuity correction when using the normal approximation to do hypothesis testing involving a bernoulli trial. The answer is vastly different (based on the answer choices given in the exam) depending on whether or not you use it. The problem does not specify to use it or to not use it, though some previous problems have specified one or the other, whereas others have not specified either.
You are given the following:
- Accidents happen during a work day at a probability of p when a machine is operated.
- The null hypothesis $H_0$ is that the probability of an accident is 0.05; the alternative hypothesis $H_1$ is that the probability is less than 0.05.
- If less than 20 accidents are observed in 365 work days, then reject the null hypothesis.
Using the normal approximation, calculate the probability of Type II error using the value 0.03 as the true probability of an accident occurring.
Any help would be greatly appreciated. Just to be clear, I am hoping to better understand when it should be used and when it should not be used, in general, in addition to learning the best way to do this problem.