4 At a doctors' surgery, the number of missed appointments per day has a Poisson distribution. In the past the mean number of missed appointments per day has been 0.9 . Following some publicity, the manager carries out a hypothesis test to determine whether this mean has decreased. If there are fewer than 3 missed appointments in a randomly chosen 5-day period, she will conclude that the mean has decreased.
- Find the probability of a Type I error.
- State what is meant by a Type I error in this context.
- Find the probability of a Type II error if the mean number of missed appointments per day is 0.2 .