Sampling Techniques (ISS (Statistical Services) Statistics Paper III): Questions 22 - 27 of 30

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Question number: 22

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2012

Essay Question▾

Describe in Detail

Discuss the allocation of a sample to different strata in stratified sampling. Explain proportional allocation and hence obtain the variance of mean of a stratified sample under proportional allocation.

Explanation

For a population consisting of N sampling units it can be divided into k relatively homogeneous sub-groups of sizesEquation , Equation , …, Equation (called as strata) such that N=Equation .

Then a simple random sample of size Equation (i = 1, 2, …, k) is drawn from

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Question number: 23

» Sampling Techniques » Simple Random Sampling With and Without Replacement

Appeared in Year: 2012

Short Answer Question▾

Write in Short

Show that for a simple random sample Equation unbiased estimate of Equation

Question number: 24

» Sampling Techniques » Probability Sampling or Random Sampling

Appeared in Year: 2012

Short Answer Question▾

Write in Short

Let Equation be the y-value of the ith unit and Equation 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

Equation

Question number: 25

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Explain circular systematic sampling. Show that minimum value of ρ is Equation , when Equation , where ρis intraclass correlation and Equation 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 kth unit in a cyclic manner till a sample of size n units is obtained, k being the integer nearest to Equation

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Question number: 26

» Sampling Techniques » Probability Sampling or Random Sampling

Appeared in Year: 2012

Short Answer Question▾

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

Essay Question▾

Describe in Detail

In simple random sampling without replacement (SRSWOR), the sample mean Equation is an unbiased estimator of population mean Equation . Obtain the variance of the estimator of the population total Y.

Explanation

Sample mean Equation is an unbiased estimator of population mean Equation i. e.

Sample mean is given by Equation

It can also be written as Equation

Where

Equation

Equation Equation

Equation

Equation

Equation

Equation

Equation

Hence Equation

Equation

Variance of the estimator of the population total Y: Equation :

Let

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