ISS (Statistical Services) Statistics Paper III: Questions 50 - 53 of 96

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Question number: 50

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

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Discuss cluster sampling. Let Equation be the sample mean based on a sample of nM elements. Equation 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 Equation with respect to Equation (without getting the derivation of V (Equation ) and V (Equation ) ). 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

… (359 more words) …

Question number: 51

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2011

Essay Question▾

Describe in Detail

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

Explanation

It is given that Equation

Equation ……………. (i)

Equation

Equation

Equation using (i)

Similarly, we will get

Equation

Equation

But Equation From (i)

Hence, Equation

Equation

Equation Equation

Equation From (i)

Auto -correlation of order k is

Equation , which is independent of k.

Hence, the process is stationary

… (2 more words) …

Question number: 52

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

Appeared in Year: 2011

Essay Question▾

Describe in Detail

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

Equation

Here Equation are considered as independently identically distributed with

Equation

Equation

…. (i)

Equation

for a plynomial Equation of mth degree

… (115 more words) …

Question number: 53

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

Appeared in Year: 2010

Short Answer Question▾

Write in Short

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

I=Equation

Where L = Lasperaye’s Price Index Number

P = Paasche’s Price Index Number.

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