Sampling Techniques (ISS 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

Short Answer Question▾

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Show that for a simple random sample s2=1n1i=1n(yiyn)2 unbiased estimate of S2.

Question number: 24

» Sampling Techniques » Probability Sampling or Random Sampling

Appeared in Year: 2012

Short Answer Question▾

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Let yi be the y-value of the ith unit and Pi 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

ŶPPS=1ni=1nyipi

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 1(n1) , when Vsy(y)=0 , where ρis intraclass correlation and y 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 N… (640 more words) …

Question number: 26

» Sampling Techniques » Probability Sampling or Random Sampling

Appeared in Year: 2012

Short Answer Question▾

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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 y is an unbiased estimator of population mean Y . Obtain the variance of the estimator of the population total Y.

Explanation

Sample mean y is an unbiased estimator of population mean Y i. e.

Sample mean is given by y=1ni=1nyi

It can also be written as y=1ni=1Nai… (382 more words) …

Question number: 28

» Sampling Techniques » Probability Sampling or Random Sampling

Appeared in Year: 2013

Essay Question▾

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 Yi= value of the ith unit of the population, i = 1,… (173 more words) …

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