5. Data on the number of accidents at a busy intersection in Waterloo over the last 5 years indicated that the average number of accidents at the intersection was 3 accidents per week. After the installation of new tIafc signals the number of accidents per week for a 25 week period were recorded as follows: 45042'01413112 221132320223 Let y; =the number of accidents in week i, i = 1,2,... ,25. To analyse these data we assume 1'} has a Poisson distribution with mean 3, i = 1,2, ,25 independently. (a) To decide whether the mean number of accidents at this intersection has changed after the installation of the new traffic signals we wish to test the hypothesis Hg. : E\" = 3. Why is the 2;. 2 li- 25 reasonable? Calculate the p-yalue for testing Hp : a1 H = 3. What would you conclude? {b} Justify the following statement: discrepance measure D = P( Y a: c) : Hz: c) where 2 ~ N(,1). J? (c) Why is the discrepance measure D = TY 3| reasonable for testing Hg. :3 = 3? Calculate the approximate pvalue using {in}. Compare this to the value in {a}