# 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

### Describe in Detail

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

## Question number: 51

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2011

### Describe in Detail

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

### Explanation

It is given that

→ ……………. (i)

using (i)

Similarly, we will get

But From (i)

Hence,

From (i)

Auto -correlation of order k is

, which is independent of k.

Hence, the process is stationary

## Question number: 52

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

Appeared in Year: 2011

### 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

Here are considered as independently identically distributed with

…. (i)

for a plynomial of m^{th} degree

## Question number: 53

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

Appeared in Year: 2010

### Write in Short

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.