# PracticeMidterms - ST 310 Midterm Exam October 14, 2008 1....

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ST 310 Midterm Exam October 14, 2008 1. Consider the following population of four units: ID 1 234 y 25 03 66 0 . (a) Enumerate (list) all possible samples of size 2, and demonstrate that ¯ y is unbiased for μ . (b) In the classical model y 1 ,...,y n i.i.d. N ( μ, σ ) , ¯ y is also unbiased for μ . Yet in the finite-population model of part (a), the variance of ¯ y is half of the variance of ¯ y in the classical model. Why? 1

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2. Briefly comment on the advisability of using a normal-approximation (nom- inal) 95% confidence interval ( ¯ y ± 1 . 96 × SE) in each of the following sce- narios: (a) Highly skewed data, n =10 , N =20 . (b) Symmetric data, no outliers, n = 900 , N = 1000 . (c) Symmetric data, no outliers, n = 100 , N , 000 . (d) Highly skewed data, n = 1000 , N = 100 , 000 . 2
3. Your client states “I know that the statistical procedures you use are unbiased, and I understand that the math guarantees that. However, I cannot believe that the estimate you’re giving me is correct, even taking standard error into ac- count.” Give the client two purely statistical and two non-statistical scenarios that could account for the apparently anomalous result. 3

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4. A stratified sample of the net worth (assets - liabilities) of 40 banks near fail- ure, and 40 financially sound banks, yields the following data, in \$B(near fail- ure = stratum 1; financially sound = stratum 2): ¯ y 1 =0 . 63 , SD 1 . 22 , ¯ y 2 = 1 . 07 , SD 2 . 34 . There are 200 banks near failure, and 1000 financially sound banks, in the population. (a) Calculate the standard error of the stratified estimator ¯ y ST in this case.
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## This note was uploaded on 01/28/2012 for the course STATISTICS 3010 taught by Professor Ooz during the Spring '11 term at Cornell University (Engineering School).

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PracticeMidterms - ST 310 Midterm Exam October 14, 2008 1....

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