2. [24 marks] a) A photocopier company kept records of the number of breakdowns per year for 100 photocopiers, giving the results Number of breakdowns 0 1 2 3 24 Frequency 8 20 37 24 11 Test at the 5% level that the above data comes from a Poisson (1 = 2) distribution. b) Two companies manufacture white board pens. A sample of 10 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 12 7.4 6.6 8.4 7.6 10.9 11.7 10.2 Company 2 9.1 13.3 8.2 11.1 10 11.6 10.5 8.7 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.c) The following table represents data on cortisol level of women in three different groups: Group 1 delivered their babies by Caesarean sectionbefore the onset of labor, Group 2 delivered by emergency Caesarean during induced labor, and group 3 experienced spontaneous labor. Group 1 262 307 211 323 454 339 304 154 287 356 Group 2 465 501 455 355 468 362 Group 3 343 772 207 1048 838 687 Use the Kruskal-Wallis test at level 0.05 to test for equality of the average cortisol level in the three groups