4 The number of sightings of a golden eagle at a certain location has a Poisson distribution with mean 2.5 per week. Drilling for oil is started nearby. A naturalist wishes to test at the \(5 \%\) significance level whether there are fewer sightings since the drilling began. He notes that during the following 3 weeks there are 2 sightings.

1. Find the critical region for the test and carry out the test.
2. State the probability of a Type I error.
3. State why the naturalist could not have made a Type II error.