Address all the questions below well

(i) In an opinion poll, a random sample is to be asked whether they favour closer ties with Europe. Determine the minimum sample size required to ensure that 95% confidence limits for the underlying population proportion are of the form "+5% ", justifying any approximations used. [4] (ii) 1,000 people took the opinion poll in part (i). 30% said "Yes" to closer ties with Europe, 50% said "No" and 20% said "Don't know". Calculate 95% confidence intervals for the proportion of the whole population holding each opinion. [4] (iii) After an extensive advertising campaign by the government another opinion poll of 800 people was taken. Of those questioned, 35% said "Yes". (a) Obtain a 90% confidence interval for the difference in proportions favouring closer ties with Europe before and after the campaign. (b) Comment on your answer. [4] [Total 12]A sample of 51 life assurance policyholders has a mean sum assured of 1 80,000 and a standard deviation of 60,000. Eight of the policyholders had a sum assured greater than 250,000. Obtain a symmetric 95% condence interval for the: [i] true mean sum assured [3] {ii} true percentage of policyholders with a sum assured greater than 250,000. [3] [Total I5] .2 You are given the following data in respect of a certain group of lives: ET 60 6 387 61 24 766 62 34 1,093 63 20 699 64 9 339 Test the hypothesis that the mortality rates of the above lives are equal to the following set which are taken from a certain standard table: Age r 4x 60 0.02287 61 0.02525 62 0.02778 63 0.03049 64 1339