# Sampling Techniques-Simple Random Sampling with and Without Replacement (ISS (Statistical Services) Statistics Paper III): Questions 1 - 5 of 5

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## Question number: 1

» Sampling Techniques » Simple Random Sampling with and Without Replacement

Appeared in Year: 2015

### Describe in Detail

Show that SRSWOR, the sample proportion is an unbiased estimator of the population proportion of members possessing a certain character. Hence obtain the variance of the estimator.

### Explanation

If we are interested in estimating the proportion of a certain character, the population of N fields can be defined with variate y _{i} as having value 1 if the field is particular characteristic, otherwise zero. If the total number of particular characteristic be N _{1} out of N

Thus,

The problem of

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## Question number: 2

» Sampling Techniques » Simple Random Sampling with and Without Replacement

Appeared in Year: 2009

### Describe in Detail

Describe the procedure of drawing a simple random sample of size n without replacement from a finite population of size N. obtain the probabilities of drawing specified sample in simple random sampling with and without replacement.

### Explanation

Procedure of drawing Simple random sampling without replacement (SRSWOR):

In SSWOR once an element is selected as a sample unit, it will not be replaced in the population pool. The selected sample units are distinct.

A sample of size is collected without replacement from the population of size . First member is chosen at random from the populat

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## Question number: 3

» Sampling Techniques » Simple Random Sampling with and Without Replacement

Appeared in Year: 2011

### Write in Short

**Explain the concept of simple random/sampling with and without replacement. In a simple Random sampling, show that is an unbiased estimator of .**

## Question number: 4

» 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: 5

» Sampling Techniques » Simple Random Sampling with and Without Replacement

Appeared in Year: 2014

### Describe in Detail

Define linear systematic sampling. Does it give equal probability of selection to all the population units? State the advantages and limitations of systematic sampling. Can a systematic sample be drawn without a physical list of population units? Justify your claim.

### Explanation

**Linear systematic sampling:**

Linear systematic sampling is a commonly employed technique if the complete and up-to date list of the sampling units is available. This consists in selecting only the first unit at random, the rest being automatically selected according to some predetermined pattern involving regular spacing of units.

Let us Suppose that

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