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4.11. To estimate the total of the variable P85 (= y) for the MU284 population, the following two-stage sampling design was used. (Stage 1) The
4.11. To estimate the total of the variable P85 (= y) for the MU284 population, the following two-stage sampling design was used. (Stage 1) The clusters in Appen- dix C were used as PSUs. A pps sample of five PSUs was drawn with selection probabilities proportional to the value of the variable TP75. (Stage 2) From each selected PSU, a aps sample of two municipalities was drawn according to Brewer's scheme with inclusion probabilities proportional to the value of the variable P75 ( = x). The following data were collected for the selected munici- palities: k Xk 33 186 10 10 187 13 14 21 117 105 102 119 26 26 43 236 88 85 239 28 28 12 68 11 12 69 66 62 48 268 84 74 270 - 74 72 (a) Compute an unbiased estimate of the total of the variable P85. (b) Compute an unbiased estimate of the variance of the estimator used in (a), as well as the corresponding cue
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