Sampling Techniques (ISS (Statistical Services) Statistics Paper III): Questions 23  28 of 30
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Question number: 23
» Sampling Techniques » Simple Random Sampling With and Without Replacement
Appeared in Year: 2012
Write in Short
Show that for a simple random sample unbiased estimate of
Question number: 24
» 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: 25
» Sampling Techniques » Simple Random Sampling and Systematic Sampling
Appeared in Year: 2013
Describe in Detail
Explain circular systematic sampling. Show that minimum value of ρ is , when , where ρis intraclass correlation and is the sample mean.
Explanation
Circular systematic sampling
This method consists of choosing a random start from 1 to N and selecting the unit corresponding to the random start and thereafter every k^{th} unit in a cyclic manner till a sample of size n units is obtained, k being the integer nearest to .
That is, if r is the number selected at random from 1 to N, the sample cons
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Question number: 26
» 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: 27
» Sampling Techniques » Simple Random Sampling and Sampling With Probability Proportional to Size
Appeared in Year: 2013
Describe in Detail
In simple random sampling without replacement (SRSWOR), the sample mean is an unbiased estimator of population mean . Obtain the variance of the estimator of the population total Y.
Explanation
Sample mean is an unbiased estimator of population mean i. e.
Sample mean is given by
It can also be written as
Where
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Question number: 28
» 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, …, N
= known value of the
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