(2009)Spiegelhalter and Barnett paper in the journal significance examined data on the daily number of homicides in London ...

     (2009)Spiegelhalter   and Barnett paper in the journal significance examined data on the daily   number of homicides in London for the 1095 days over the three year period   from April 2004 to march 2007. The frequency distribution of the daily   numbers of homicides is given in the table below. Number of homicides   :Frequency. 0:713 , 1:299, 2:66, 3:16, 4:1 , >=5:0 (i) carry out a   chi-square goodness of fit test to test the hypothesis that the data may be   regarded as a random sample from a poisson distribution. Draw conclusions   (ii) As an alternative to the (chi-square goodness of fit test), carry out a   dispersion test to test the same hypothesis. (iii) Given the data and   hypothsis, and assuming that the underlying pattern of homicides remains   unchanged over the subsequent month,state what is the estimate distribution   of the total number of homicides in london for the month of april 2007.   estimate correct to 2 decimal places the probability that there are 20 or   more homicides in april 2007.