Provide step by step answers to the following questions.

The mortality experience of some whole of life assurance policyholders has been compared with a standard mortality table for assured lives. The following is an extract from the data: Age, X Actual deaths, Expected deaths, 0, - E,q Ox 37 42.88 -5.88 40 61.73 -21.73 28 38.06 -10.06 41 47.23 -6.23 40.36 -6.36 49.98 -9.98 25.13 1.87 22.25 -7.25 26.23 -10.23 30 27.61 2.39 70 23 25.11 -2.11 Total 331 406.56 -75.57 (i) Carry out a comparison between the actual and expected mortality experience, using the following statistical tests: (a) Chi-squared test (b) Cumulative deviations test (c) Serial correlations test. You should state the appropriate null hypothesis and, for each test, the conclusion reached with regard to this hypothesis. [12] (ii) Summarise what you can infer about the mortality experience of these policyholders from your analysis, giving your reasons. [3](iii) You have now decided to produce graduated rates of mortality by fitting the following function to these data using weighted least squares techniques: g (x ) = aqx (a) Determine the value of the parameter a that minimises the weighted least squares criterion for these data. (b) The graduated rates are to be tested using the same tests as in part (i). Without performing any further calculations, state how you would expect the results to differ, if at all, from the results of the tests you carried out in part (i). (c) Hence state whether you think this graduation is likely to be satisfactory, giving your reasons. [6]