ISS (Statistical Services) Statistics Paper III: Questions 49 - 53 of 109

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Question number: 49

» Sampling Techniques » Stratified Random Sampling

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Appeared in Year: 2010

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What is PPS Sampling? Explain why such type of sampling is needed? Describe Lahiri’s method for PPS selection of sample.

Question number: 50

» Sampling Techniques » Cluster Sampling with SRS - Intra-Class Correlation Coefficient

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Appeared in Year: 2011

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Discuss cluster sampling. Let be the sample mean based on a sample of nM elements. is the sample mean based on a sample of nM elements drawn for SRS without replacement from NM elements in the population. Obtain Relative efficiency of with respect to (without getting the derivation of V ( ) and V ( ) ). Write its ANOVA table.

Explanation

Cluster sampling:

Cluster sampling is a type of sampling method. If the population size is very large, the samplings lead to several difficulties. It might be tough to prepare a frame for large population size. In such case the, cluster sampling is used. In this method, the population is divided into separate groups, called clusters. Then, a simp

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Question number: 51

» Econometrics » Autoregressive Linear Regression

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Appeared in Year: 2011

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Let , - ∞ < t < ∞, where are i, i. d. with and . Show that the process is stationary with correlation.

Explanation

It is given that

→ ……………. (i)

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Question number: 52

» Applied Statistics » Time Series Analysis » Exploratory Time Series Analysis

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Appeared in Year: 2011

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Give the various steps for finding the variance of the random component using variate difference method. Is F-test used for testing the significance of homogeneity of two successive estimates of variance? If yes, ok, otherwise which ‘test can be used? Discuss.

Explanation

To find the variance of the random component using variate difference method:

let us consider a series represented as the sum of functional part and random component

Here are considered as independently identically distributed with

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Question number: 53

» Applied Statistics » Index Numbers » Price Relatives and Quantity or Volume Relatives

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Appeared in Year: 2010

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What are the three tests of index numbers? Verify whether the following index number satisfies any of these tests:

I=

Where L = Lasperaye’s Price Index Number

P = Paasche’s Price Index Number.