Question 1:
a) Explain a procedure of drawing a sample by two stage sampling and give an example. Describe the applications of two-stage sampling.
b) In sampling with PPS with replacement obtain the estimator of the population total. Derive its variance.
Question 2:
a) What is PPS sampling? Explain Cahiri's method of PPS sampling. In PPS sampling with replacement define an unbiased estimator of population mean.
b) Derive the variance of the estimated mean in two-stage sampling.
Question 3:
a) Describe ratio estimation in stratified sampling. Define a combined ratio estimator for the population total and obtain the expression for the large sample variance of the estimator.
b) Explain simple regression estimate of the population mean. It is unbiased? If not point out when it is unbiased?
Question 4:
a) Discuss critically the use of auxiliary information with theoretical justification supported by some illustrate examples.
b) Discuss the relative efficiencies of ratio and regression estimates.
Question 5: Write short notes on any two of the following:
a) CSO.
b) Gain in precision due to stratification.
c) Multistage sampling.
d) Random number tables and their use.
e) Bias and mean square error of ratio estimator.