454as2 - STAT 854/454 Sampling Theory and Practice...

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Unformatted text preview: STAT 854/454 Sampling Theory and Practice Assignment 2 Due: Tuesday, February 8, in class Format: standard letter size paper, single-sided, with a cover page 1. Consider a stratified population with H = 3, N 1 = 500, N 2 = 1000, N 3 = 1500. Suppose that we know the stratum population variance σ 2 y 1 = 100, σ 2 y 2 = 200, σ 2 y 3 = 225. We like to take a stratified simple random sample. (a) Let n = 84. Find the proportional sample size allocation and compute V prop (¯ y st ). (b) Let n = 84. Find the Neyman allocation, compute V neym (¯ y st ). (c) Suppose further that the three stratum population means are all equal, and we take a sample of size n = 84 from the (unstratified) population using SRSWOR. Let ¯ y be the sample mean. Find V (¯ y ). (d) Compare the values of V prop (¯ y st ), V neym (¯ y st ), V (¯ y ) and make appropriate comments. 2. ( STAT 854 only! ) Neyman allocation based on an auxiliary variable: The execution of the Neyman allocation requires the knowledge of stratum variances σ 2 yh , h = 1 , 2 , ··· ,H . In practical situations those quantities are unknown, but values of certain auxiliary variables...
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This note was uploaded on 02/04/2011 for the course STAT 454 taught by Professor Da during the Spring '09 term at Waterloo.

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454as2 - STAT 854/454 Sampling Theory and Practice...

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