Solve the following questions. Kindly address all the questions.

(i) Explain why graduated rates, rather than crude estimates of mortality rates are used in the construction of standard mortality tables. [3] (ii) A graduation of the mortality experience of the male population of a region of the United Kingdom has been carried out using a graphical method. The following is an extract from the results. Actual Initial Graduated Age number of mortality rate exposed to deaths risk 4 x Ex4x 14 3 0.00038 12,800 4.86 8 0.00043 15,300 6.58 5 0.00048 12,500 6.00 14 0.00053 15,000 7.95 17 0.00059 16,500 9.74 19 9 0.00066 10,100 6.67 20 15 0.00074 12,800 9.47 21 10 0.00083 13,700 11.37 22 10 0.00093 11,900 11.07 Total 91 73.71 Use the Chi-squared test to test the adherence of the graduated rates to the data. State clearly the null hypothesis you are testing and comment on the result. [4] (iii) Perform two other tests which detect different aspects of the adherence of the graduation to the data. For each test state clearly the features of the graduation which the test is able to detect, and comment on your results. [8] [Total 15]If 6 =0.01r for 0