# ISS (Statistical Services) Statistics Paper III: Questions 29 - 33 of 109

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## Question number: 29

» Sampling Techniques » Concepts in Sampling

Appeared in Year: 2010

### Describe in Detail

What precautions would you take in planning for a sample survey?

### Explanation

Precautions to be taken for planning sample survey:

**Objectives of the survey:**The first step is to define clearly the objective of the survey. The objective should be kept easy so that the people working for the survey easily understand it. The hypothesis being tested and the outcomes that will be used to study the hypothesis should be clear.**Definin**

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## Question number: 30

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2011

### Describe in Detail

Discuss second order autoregressive series. For this series, obtain complementary function (CF) only.

### Explanation

Second order autoregressive series:

Sometimes, the values of a time series data are highly correlated with the values that precede and succeed them. i. e. , The value of a time series at any time “t” may depend upon its own value at times t-1, t-2, …, t-k, the relationship being linear.

In such cases an auto-regression model is used for forecasting.

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## Question number: 31

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2010

### Write in Short

A hypothetical population has the population units in linear trend given by = a (i = 1,2, … N).

Show that: V (

V ( where N = nk

V (

Hence, deduce that

## Question number: 32

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

Appeared in Year: 2011

### Write in Short

For the following table:

Commodity

A | B | |

| 1 | 1 |

| 10 | 5 |

| 2 | x |

| 5 | 2 |

Where p and q stand for price and quantity for 0 and 1 time periods respectively. Find the value of X if the ratio between Laspeyre’s (L) and Paasche’s (P) index number is L: P: : 28: 27

## Question number: 33

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2010

### Describe in Detail

Explain the concept of stratification in stratified simple Random sampling. What is proportional and optimum allocation in stratified simple Random sampling? With usual notations show that: V ( ) _{opt} < V ( ) _{prop} < V ( ) _{ran}

### Explanation

**Stratification:**

Stratification means division into layers, classes or categories. Past or some other information related to the character under study may be used to divide the population into various groups. Then simple random sampling or systematic sampling is applied within each stratum.

The strata should be mutually exclusive and exhaustive: every

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