Part B In order to estimate the mean number of people per household in a district of 80,000 households, we select a sample of 4 villages from 600 villages in this district. These villages are selected with unequal probabilities proportional to their size (number of households). The 4 villages selected have respectively 100, 200, 400, 800 households. Within each of the 4 villages selected, 10% of the households are selected with a simple random sampling design. i) Which sampling design has been used? [2] ii) What are the inclusion probabilities of the households selected? [5] iii) The sample mean of the number of people per household in each of the samples for the 4 villages selected is respectively: 1.8, 2.0, 1.6 and 1.5. Give an estimate of the mean number Y of people per household in this district. Justify your answer. [8] [Total 25]