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

Short Answer Question▾

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

Short Answer Question▾

Write in Short

Let be the y-value of the ith 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

Essay Question▾

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 kth 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

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 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

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 = value of the ith unit of the population, i = 1,2, …, N

= known value of the

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