## Introduction- Survey sampling

Population- the population is the collection or group of observations under study in a survey sampling.

The total number of observations in a population is the population size and we denote this by N.

## Types of population

1. finite population – the population contains finite numbers of observations is the finite population

2. Infinite population- it contains infinite number of observations.

3. Real population- the population which comprises the items which are all present physically is the real population.

4. Hypothetical population- if the population consists the items which are not physically present but we can imagine their existence, we call it as hypothetical population.

## Sample

To get the information from all the elements of a large population may be time consuming and difficult.

And also if the elements of population are destroyed under investigation then getting the information from all the units is not make a sense. For example, to test the blood, doctors take very small amount of blood.

## Complete survey

When we investigate or study each and every element of the population for the characteristics under study then we call it complete survey or census.

## Survey sampling

When study a part or a small number of elements of population for the characteristics under study then we call it sample survey or sample enumeration Simple Random Sampling or Random Sampling

The simplest and most common method of sampling is simple random sampling.

In simple random sampling, the sample is drawn in such a way that each element or unit of the population has an equal and independent chance of being included in the sample. If a sample is drawn by this method then it is known as a simple random sample or random sample

## Simple Random Sampling without Replacement (SRSWOR)

In simple random sampling, if we select elements one by one in such a way that an element or unit drawn at a time is not replace back to the population before the subsequent draws, we say it as SRSWOR.

Suppose we draw a sample from a population, the size of sample is n and the size of population is N, then total number of possible sample is NCn.

## Simple Random Sampling with Replacement (SRSWR)

In simple random sampling, if we draw elements one by one in such a way that a unit drawn at a time is replaced back to the population before the subsequent draw is called SRSWR.

Suppose we draw a sample from a population, the size of sample is n and the size of population is N, then total number of possible sample is .

## Parameter

A parameter is a function of population values which we use to represent the certain characteristic of the population. For example, population mean, population variance, population coefficient of variation, population correlation coefficient, etc. are all parameters. Population parameter mean usually denoted by μ and population variance denoted by

## Sample mean and sample variance

Let X1, X2, X3,……Xn be a random sample of size n from a population whose pmf or pdf function

the sample mean is-

And sample variance-

## Statistic

Any quantity which does not contain any unknown parameter and we calculate it from sample values, we say it as statistic.

Suppose X1, X2,…. Xn is a random sample of size n from a population with mean μ and variance then the sample mean

Is a statistic.

## Estimator and estimate

if a statistic is used to estimate an unknown population parameter then it is known as estimator and the value of the estimator based on observed value of the sample is known as estimate of parameter.

## Standard error

The standard deviation of the sampling distribution is a standard error.

When we increase the sample size then standard increases.

It plays an important role in large sample theory.

If the size of the sample is less than 30, we consider it as small sample otherwise it is a large sample.

We assume the sampling distribution of large samples as normal.

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