# ST3239 - NATIONAL UNIVERSITY OF SINGAPORE EXAMIN ATION...

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------------------------- NATIONAL UNIVERSITY OF SINGAPORE EXAMIN ATION ST3239 Survey Methodology April 2009 Time allowed: 2 hours INSTRUCTIONS TO CANDIDATES 1. This examination paper contains Four (4) questions and comprIses Fourteen (14) printed pages. 2. Answer ALL questions. Marks for each question are indicated at the beginning of the question. 3. Candidates may use calculators. However, they should layout systematically the vari - ous steps in the calculations. 4. This is a CLOSED BOOK examination. Candidates are allowed to bring T\VO help pages written on BOTH sides. Matriculation No. 1 2 3 4 T!

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PAGE 2 ST3239 1. [25 points] Consider drawing a stratified random sample with a linear cost function L C=CO+ L~ni' i=l (a) Show that the variance of fist is minimum for a specified cost C or the cost is minimum for a specified V = V (fJst) if for each i = 1,2, ... ,L, (b) From this, find the expression of the sample size n for optimal sampling scheme for a given C and for a given V.
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