Sampling TechniquesProbability Sampling or Random Sampling (ISS (Statistical Services) Statistics Paper III): Questions 1  4 of 4
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Question number: 1
» Sampling Techniques » Probability Sampling or Random Sampling
Appeared in Year: 2011
Describe in Detail
Discuss Lahiri’s method of selecting samples for PPS scheme. Give a suitable example to select
4 units when N = 10, M = 60, by taking your choice of sample number and its corresponding size.
Explanation
Lahiri’s Method of selecting samples for PPS scheme:
Let M = max maximum of the sizes of N units in the population (i = 1, 2, …10)
Steps involved in selecting samples:
1) Select a random number i from 1 to N
2) Select one more random number j,
Question number: 2
» Sampling Techniques » Probability Sampling or Random Sampling
Appeared in Year: 2012
Write in Short
Let be the yvalue of the i^{th} unit and be corresponding selection probability,
i = 1, 2, …, N. Then, based on a sample of size n drawn with replacement, show that an unbiased estimator for population total is
Question number: 3
» Sampling Techniques » Probability Sampling or Random Sampling
Appeared in Year: 2012
Write in Short
Obtain an unbiased estimator of the gain due to PPSWR sampling as compared to SRSWR.
Question number: 4
» Sampling Techniques » Probability Sampling or Random Sampling
Appeared in Year: 2013
Describe in Detail
Give the names of various procedures for selecting a sample using probability proportional to size (PPS) scheme. Obtain an unbiased estimator of the population mean under PPS.
Explanation
Procedures for selecting a sample using probability proportional to size (PPS) scheme are:

PPS sampling with Replacement

PPS sampling without Replacement

Cumulative total method

Lahiri’s method
An unbiased estimator of the population mean under PPS:
Let = value of the ith unit of the population, i = 1, 2,