# Sampling Techniques-Probability Sampling or Random Sampling (ISS Statistics Paper III): Questions 1 - 4 of 4

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## Question number: 1

» Sampling Techniques » Probability Sampling or Random Sampling

Appeared in Year: 2011

Essay Question▾

### 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,… (304 more words) …

## Question number: 2

» 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: 3

» 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: 4

» 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,… (96 more words) …

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