Question 3 [25 marks] The purpose is to estimate the mean net annual income exclusively from a population of 100 farms. For a simple random sample of 9 farms, the following data relate to farm size (X), and net annual income (Y). 69 71 89 95 4 14 2 7 7092 65 73 Sampled farm (ID): X (in 100 acres): Y (in 1000): 7 13 34 45 56 7 6 13 4 6 76 74 85 68 72 69 71 Moreover, we know that the population mean of X is equal to 8.5 acres. i) Define the ratio estimator of the population mean of the variable Y. Define all symbols used. [4] ii) Calculate the ratio estimate of the population mean of the variable Y. [4] iii) Estimate the variance of the ratio estimator defined in i). [7] iv) Is the variance of the ratio estimator larger than the variance of the simple expansion estimator? Justify your answer. [10]