7 In the past the number of accidents per month on a certain road was modelled by a random variable with distribution \(\operatorname { Po } ( 0.47 )\). After the introduction of speed restrictions, the government wished to test, at the 5\% significance level, whether the mean number of accidents had decreased. They noted the number of accidents during the next 12 months. It is assumed that accidents occur randomly and that a Poisson model is still appropriate.

1. Given that the total number of accidents during the 12 months was 2 , carry out the test.
2. Explain what is meant by a Type II error in this context.
   It is given that the mean number of accidents per month is now in fact 0.05 .
3. Using another random sample of 12 months the same test is carried out again, with the same significance level. Find the probability of a Type II error.