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

Essay Question▾

Describe in Detail

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

Explanation

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

Sample mean is given by Equation

It can also be written as Equation

Where

Equation

Equation Equation

Equation

Equation

Equation

Equation

Equation

Hence Equation

Equation

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

Let

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