Data Collectionhard
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A small survey of 5 companies uses unequal probability sampling with inclusion probabilities: \pi_1 = 0.5, \pi_2 = 0.4, \pi_3 = 0.3, \pi_4 = 0.2, \pi_5 = 0.1. Companies 1, 3, and 5 are sampled with observed annual sales: y_1 = 500K,y3=500K, y_3 = 300K, y_5 = $100K. Using the Horvitz-Thompson estimator Y^HT=iSyiπi\hat{Y}_{HT} = \sum_{i \in S} \frac{y_i}{\pi_i} the estimated total population sales is: