Refer to the attachments below to solve the questions that follow. Ensure precision in your answers.

The input-output ratio coefficients for a three sector economy are given as: 1 11 212 2131 10.2 0.3 0.2 = 0.4 0.1 0.2 while the final demand matrix is given as: A =321 a72 a23 a33 (0.1 0.3 0.2) az3 232 10 D = 5 Determine the total output required in each of the three sectors to meet the inter- industry input requirements and the final demand.It is desired to investigate the level of premium charged by two companies for contents policies for houses in a certain area. Random samples of 10 houses insured by Company A are compared with 10 similar houses insured by Company B. The premiums charged in each case are as follows: Company A 117 154 166 189 190 202 233 263 289 331 Company B 142 160 166 188 221 241 276 279 284 302 For these data: A = 2,134. _ A? = 494.126. _ B = 2.259. _ B2 = 541,463. (i) Illustrate the data given above on a suitable diagram and hence comment briefly on the validity of the assumptions required for a two-sample r test for the premiums of these two companies. (ii) Assuming that the premiums are normally distributed, carry out a formal test to check that it is appropriate to apply a two-sample / test to these data. (iii) Test whether the level of premiums charged by Company B was higher than that charged by Company A. State your p-value and conclusion clearly. (iv) Calculate a 95% confidence interval for the difference between the proportions of premiums of each company that are in excess of f200. Comment briefly on your result. (v) The average premium charged by Company A in the previous year was f170. Formally test whether Company A appears to have increased its premiums since the previous year