# Sampling Techniques-Simple Random Sampling and Sampling With Probability Proportional to Size (ISS (Statistical Services) Statistics Paper III): Questions 1 - 1 of 1

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## Question number: 1

» Sampling Techniques » Simple Random Sampling and Sampling With Probability Proportional to Size

Appeared in Year: 2013

### Describe in Detail

In simple random sampling without replacement (SRSWOR), the sample mean** **is an unbiased estimator of population mean** . **Obtain the variance of the estimator of the population total Y.

### Explanation

Sample mean is an unbiased estimator of population mean i. e.

Sample mean is given by

It can also be written as

Where

Hence

**Variance of the estimator of the population total Y: ****: **

Let us denote the Population Total Y as

The estimate of population total Y can be obtained by multiplying the estimate of mean by population size N.

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