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An insurance company is investigating past data for two household claims assessors. A and B, used by the company. In particular claims resulting from similar types of water damage were extracted. The following table shows the assessors' initial estimates of the cost (in units of $100) of meeting each claim. A: 4.6 6.6 2.8 5.8 2.1 5.2 5.9 34 7.8 3.5 1.6 8.6 2.7 B: 5.7 34 4.7 3.6 6.5 3.3 3.8 2.4 7.0 4.0 4.4 for the A data: MA = 13, Ex = 60.6 and Ex= 340.92 for the B data: Mp - 11, Ex = 48.8 and Ex- = 236.80 (i) Draw a suitable diagram to represent these data so that the initial estimates of the two assessors can be compared. [2] (ii) You are required to perform an appropriate test to compare the means of the assessors' initial estimates for this type of water damage. (a) State your hypotheses clearly. (b) Use your diagram in part (i) to comment briefly on the validity of your test. (0) Calculate your test statistic and specify the resulting P-value. (d) State your conclusion clearly. [10] (iii) You are required to perform an appropriate test to compare the variances of the assessors' initial estimates. (a) State your hypotheses clearly. (b) Use your diagram in part (i) to comment briefly on the validity of your test. (9) Calculate your test statistic and specify the resulting P-value. (J) State your conclusion clearly and hence comment further on the validity of your test in part (ii). 171 (iv) Use your answers in parts (i) to (iii) to comment on the overall comparison of the two assessors as regards their initial estimates for this type of water damage. [Total 20]An investigation was conducted into the effect marriage has on mortality and a model was constructed with three states: 1 Single, 2 Married and 3 Dead. It is assumed that transition rates between states are constant. (i) Sketch a diagram showing the possible transitions between states. [2] (ii) Write down an expression for the likelihood of the data in terms of transition rates and waiting times. defining all the terms you use. [3] The following data were collected from information on males and females in their thirties. Years spent in Married state 40.062 Years spent in Single state 10,298 Number of transitions from Married to Single 1.382 Number of transitions from Single to Dead 12 Number of transitions from Married to Dead 9 (Hil) Derive the maximum likelihood estimator of the transition rate from Single to Dead. [4] (iv) Estimate the constant transition rate from Single to Dead and its variance. [2] [Total 11|