# Sampling Techniques (ISS (Statistical Services) Statistics Paper III): Questions 18 - 22 of 30

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## 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, such that

3) If , then i^{th} unit is selected, otherwise the pair (i, j) is rejected and an

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## 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 into separate groups, called clusters. Then, a simp

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## 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.

## Question number: 22

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2012

### Describe in Detail

Discuss the allocation of a sample to different strata in stratified sampling. Explain proportional allocation and hence obtain the variance of mean of a stratified sample under proportional allocation.

### Explanation

For a population consisting of N sampling units it can be divided into k relatively homogeneous sub-groups of sizes, , …, (called as strata) such that N=.

Then a simple random sample of size (i = 1,2, …, k) is drawn from each of the stratum such that n=, and this sample is the stratified random sample of size n.

**Allocati**

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