Statistical Inference

2. [23 marks] i) [11 marks] On a busy Sydney crossroad, traffic accidents happen almost every week. The distribution of the number of accidents in a week is believed to be Poisson. The traffic accident data has been summarized in the following table: Number of accidents | 0 |1 2 1>3 Frequency 6 9 8 3 Test at the 5% level that the above data comes from a Poisson (1 = 1.5) distribution. ii) [12 marks] Two companies manufacture white board pens. A sample of 9 pens from one company and 8 pens from the other were tested until they were no longer readable. The results (in hours) were: Company 1 8.9 9.9 7.4 6.6 8.4 7.6 10.9 11.7 10.2 Company 2 9.1 13.3 8.2 10 11.6 10.5 8.7 9.7 Using the Wilcoxon Test for large samples, test at the 5% level the hy- pothesis that there is no difference between the two company's pens, against the one-sided alternative that the pens of company 2 last longer