# Sampling Techniques [ISS (Statistical Services) Statistics Paper III]: Questions 1 - 4 of 30

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## Question number: 1

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2015

### Describe in Detail

Explain the principles of forming strata and clusters. What are the difference between stratified sampling and clusters sampling?

### Explanation

The principles of forming strata for a population are summarized below:

(i) The strata should be non-overlapping and should together comprise the whole population.

(ii) The stratification of population should be done in such a way that strata are homogenous within themselves.

(iii) If the limit of precision for certain sub-populations is given, it wil

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## Question number: 2

» Sampling Techniques » Multistage Sampling and Its Application

Appeared in Year: 2015

### Describe in Detail

Consider a population U= {u _{1}, u _{2}, …, u _{n}}. Observations of study variable (y) and auxiliary variable (x) are y (u _{i}) =y _{i}, x (u _{i}) =x _{i}, i = 1,2, . . , N. Let p _{i} =X _{i} /X where . A sample of size n is drawn with PPSWR. Show that the population total , the estimator is an unbiased estimator. Obtain the variance of the estimator of the population total.

### Explanation

Consider a population U= {u _{1}, u _{2}, …, u _{n}}. Observations of study variable (y) and auxiliary variable (x) are y (u _{i}) =y _{i}, x (u _{i}) =x _{i}, i = 1,2, . . , N. Let p _{i} =X _{i} /X where be the probability that unit is selected in a sample such that . Let n independent selections be made with replacement method and the

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## Question number: 3

» 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: 4

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2015

### Describe in Detail

What are the advantages of stratified sampling? Consider the allocation of sample size n _{i} of strata given by , where N _{i} is the stratum size, σ _{i} is the within stratum standard deviation of the ith stratum, (i = 1,2, …, k) and δ real. Write down the expression for the where stands for the unbiased estimator of the population mean of the study variate y based on sample random sample without replacement in each stratum.

### Explanation

In this type of sampling method first the whole population is divided into homogeneous groups under certain criterion. There groups are termed as strata. Many advantage of stratified sampling can be summarized as follows.

(i) if the admissible error is given, small samples is needed which results into a cut of expenditure.

(ii) In case the cost of su

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