1011SEM2-ST3239 - NATIONAL UNIVERSITY OF SINGAPORE...

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· . NATIONAL UNIVERSITY OF SINGAPORE EXAMINATION ST3239 - Survey Methodology (Semester II: 2010-2011) April 2011 Time Allowed: 2 Hours INSTRUCTIONS TO CANDIDATES 1. This examination paper contains Five (5) questions on THREE (3) pages includ - ing the cover page. 2. Answer ALL the questions for TOTAL 100 marks. 3. All NOTATIONS used here are the same as those used in the lecture notes. 4. Write your answers neatly ON THE ANSWER BOOK. 5. This is a closed textbook and notes examination. The students are allowed to bring two A4 size help sheets with both sides written. Only non-programmable calculators are allowed. 1
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ST3239 Unless otherwise stated, use 5% as the significance level and ZO.025 = 2. 1. (a). (10%) Suppose {Y1,'" ,Yn} is a simple random sample from a population with population size N. Also assume that the mean J.ly of this population is known. Find an unbiased estimator for Var(O), where 0 = n- 1 2:7=1 (Yi J.ly)2. (b). (10%) Suppose that we wish to estimate the total number of the fish N in a lake. Let t be number of fish captured and tagged in the
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