Survey Sampling Exam
Budget: €30 – €250 EUR
From the population U = f1; 2; 3g a sample s = s1 [ s2 is
selected according to the following two-stage procedure:
1. a sample s1 of size n = 1 is selected from U by the SRS design;
2. a sample s2 is selected from U n s1 by the BES design with π = 1=8.
Let y be a study variable with values y1 = 10, y2 = 5, and y3 = 20.
(a) Determine the sampling design p(·).
(b) Check whether the design is proper and measurable.
(c) Compute the expected sample size E(nS).
(d) Compute the expectation and the bias of btalt = N
Pk2s y˘k
Pk2s 1=πk as an estimator for the
population total t
selected according to the following two-stage procedure:
1. a sample s1 of size n = 1 is selected from U by the SRS design;
2. a sample s2 is selected from U n s1 by the BES design with π = 1=8.
Let y be a study variable with values y1 = 10, y2 = 5, and y3 = 20.
(a) Determine the sampling design p(·).
(b) Check whether the design is proper and measurable.
(c) Compute the expected sample size E(nS).
(d) Compute the expectation and the bias of btalt = N
Pk2s y˘k
Pk2s 1=πk as an estimator for the
population total t