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As part of an investigation into health service funding a working party was concerned with the issue of whether mortality rates could be used to predict sickness rates. Data on standardised mortality rates and standardised sickness rates were collected for a sample of 10 regions and are shown in the table below: Region Mortality rate m (per 10.000) Sickness rate s (per 1.000) 125.2 206.8 119.3 213.8 125.3 197.2 111.7 200.6 117.3 189.1 100.7 183.6 108.8 181.2 102 0 168.2 104.7 165.2 121.1 228.5 Data summaries: Em - 1136.1, Em - 129,853.03, Es - 1934.2, Es - 377,700.62, Emis - 221,022.58 (1) Calculate the correlation coefficient between the mortality rates and the sickness rates and determine the probability-value for testing whether the underlying correlation coefficient is zero against the alternative that it is positive. [4] (ii) Noting the issue under investigation, draw an appropriate scatterplot for these data and comment on the relationship between the two rates. (3] (iii) Determine the fitted linear regression of sickness rate on mortality rate and test whether the underlying slope coefficient can be considered to be as large as 2.0. [5] (iv) For a region with mortality rate 115.0. estimate the expected sickness rate and calculate 95% confidence limits for this expected rate. (4] [Total 16]Individual claims under a certain type of insurance policy are for either I (with probability a) or 2 (with probability ] - o). The insurer is considering entering into an excess of loss reinsurance arrangement with retention 1 + k (where