# Sampling Techniques (ISS (Statistical Services) Statistics Paper III): Questions 17 - 21 of 30

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## Question number: 17

» 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 =

## Question number: 18

» Sampling Techniques » Probability Sampling or Random Sampling

Appeared in Year: 2011

### Describe in Detail

Discuss Lahiri’s method of selecting samples for PPS scheme. Give a suitable example to select

4 units when N = 10, M = 60, by taking your choice of sample number and its corresponding size.

### Explanation

** Lahiri’s Method of selecting samples for PPS scheme: **

Let M = max maximum of the sizes of N units in the population (i = 1, 2, …10)

Steps involved in selecting samples:

1) Select a random number i from 1 to N

2) Select one more random number j,

## Question number: 19

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2010

### Write in Short

What is PPS Sampling? Explain why such type of sampling is needed? Describe Lahiri’s method for PPS selection of sample.

## Question number: 20

» Sampling Techniques » Cluster Sampling With SRS - Intra-Class Correlation Coefficient

Appeared in Year: 2011

### Describe in Detail

Discuss cluster sampling. Let be the sample mean based on a sample of nM elements. is the sample mean based on a sample of nM elements drawn for SRS without replacement from NM elements in the population. Obtain Relative efficiency of with respect to (without getting the derivation of V () and V () ). Write its ANOVA table.

### Explanation

Cluster sampling:

Cluster sampling is a type of sampling method. If the population size is very large, the samplings lead to several difficulties. It might be tough to prepare a frame for large population size. In such case the, cluster sampling is used. In this method, the population is divided

## Question number: 21

» 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.