# 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 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

### 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 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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