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

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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 are often known. For simplicity, we assume
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