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practice_final - ST 310 Final Exam Due no later than(in...

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ST 310 Final Exam Due no later than December 15, 2007 (in electronic or paper form). Do 4 problems of your choice. 1. Adaptive cluster sampling. Consider the population given in the attached spreadsheet. A unit (square) “satisfies the condition” if a 1 is present, oth- erwise not. The sampling frame is a 25 × 25 grid; a simple random sample of n = 20 of these squares produces the sample coordinates given (i.e., we sample the corresponding grid squares). For various reasons, it is not eco- nomically feasible in this application to use the sample “geometry” given in the text; instead, one of the two patterns given in the spreadsheet must be used. Carry out the adaptive cluster sampling procedure until it terminates, for each of the two patterns (separately). Is either “better” in this case? Would there be any way to choose one of the patterns a priori ? 2. A large grocery-store chain wishes to audit its price scanners. A simple ran- dom sample of n = 50 orders (receipts) is selected and carefully audited, with results (receipts) given in the attached spreadsheet: “recorded” means the re- ceipt recorded by the computer based on the scanner data (from the cashier’s scans of the items); ”actual” means the actual receipt based on hand-checking every item against its actual (official) price. The long-run average scanner- based receipt (from database records) is $62.11. Use two different strategies to estimate the true, actual average receipt, and give associated standard er- rors. Comment on the relative precision of these two estimates. 3. In a forest study to determine quantity of a certain kind of timber, the for- est region is subdivided into polygons according to natural and artificial map boundaries. A random sample of polygons is then selected by PPSWR (prob- ability proportional to size with replacement) sampling, the quantity of har- vestable timber in the polygon is measured, and the total timber quantity in 1
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the forest is estimated. Data from a sample of 10 such polygons, along with their sizes (expressed as a proportion of the population = probability of se- lection on one draw) is given in the attached spreadsheet. Compute the first- order inclusion probabilities π i for the sample units, and hence compute the Horvitz-Thompson estimate of the population total τ . ( Hint
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