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consider a population with N = 4 with the y-values 55,76,99 and 120, respectively an dthe true population total Y = 350 . The corresponding Pi's are given by 0.1, 0.2, 0.3 and 0.4 respectively. Also, consider PPSWOR sampling with n = 2. The inclusion probabilities are derived as pi-1 = 0.2345 and pi-2 = 0.4413 , pi-3 = 0.6083 and pi-4 = 0.7159. Suppose units 2 and 3 are in the sample, so that the Horvitz-Thomson estimate Y-HT of the population total Y is 334.967. The variance estimate v1 (Y Ht) of this estimator is (up to 2 decimal place).   a). 10638.09   b). 26945.6   c).8153.75   d). -10638.09

consider a population with N = 4 with the y-values 55,76,99 and 120, respectively an dthe true population total Y = 350 . The corresponding Pi's are given by 0.1, 0.2, 0.3 and 0.4 respectively. Also, consider PPSWOR sampling with n = 2. The inclusion probabilities are derived as pi-1 = 0.2345 and pi-2 = 0.4413 , pi-3 = 0.6083 and pi-4 = 0.7159. Suppose units 2 and 3 are in the sample, so that the Horvitz-Thomson estimate Y-HT of the population total Y is 334.967. The variance estimate v1 (Y Ht) of this estimator is (up to 2 decimal place).   a). 10638.09   b). 26945.6   c).8153.75   d). -10638.09

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 14E
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consider a population with N = 4 with the y-values 55,76,99 and 120, respectively an dthe true population total Y = 350 . The corresponding Pi's are given by 0.1, 0.2, 0.3 and 0.4 respectively. Also, consider PPSWOR sampling with n = 2. The inclusion probabilities are derived as pi-1 = 0.2345 and pi-2 = 0.4413 , pi-3 = 0.6083 and pi-4 = 0.7159. Suppose units 2 and 3 are in the sample, so that the Horvitz-Thomson estimate Y-HT of the population total Y is 334.967. The variance estimate v1 (Y Ht) of this estimator is (up to 2 decimal place).

 

a). 10638.09

 

b). 26945.6

 

c).8153.75

 

d). -10638.09

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