# Sampling Techniques-Simple Random Sampling and Systematic Sampling (ISS (Statistical Services) Statistics Paper III): Questions 1 - 5 of 5

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## Question number: 1

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2010

### Write in Short

A hypothetical population has the population units in linear trend given by = a (i = 1,2, … N).

Show that: V (

V ( where N = nk

V (

Hence, deduce that

## Question number: 2

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2011

### Describe in Detail

Explain aligned sample and unaligned systematic sampling method

### Explanation

Systematic sampling in two dimensions:

The linear systematic sampling can be extended for two dimensions populations. here it is assumed that the n m k l population units are arranged in the form of ml rows, each containing nk units and a systematic sampling of m n units is selected. There are two procedures adopted to draw a sample of size mn.

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## Question number: 3

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2010

### Describe in Detail

Explain the concepts of linear and circular systematic sampling giving suitable illustrations.

Further, show that for linear systematic sampling, sample mean is an unbiased estimator for population mean.

### Explanation

Let us suppose that N sampling units are serially numbered from 1 to N in some order and a sample of size n is to be drawn in such a way that N is expressible as a product of two integers *n* and *k. *

N = nk → k = Where k, usually called the sampling interval. k is taken as the integer nearest to

**Linear systematic sampling: **

To draw a sample of

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## Question number: 4

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2012

### Write in Short

Show that mean of a systematic sample is more precise than the mean of a simple random sample of size n under a certain condition to be obtained by you.

## Question number: 5

» 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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