# ISS (Statistical Services) Statistics Paper III: Questions 24 - 31 of 109

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## Question 24

Appeared in Year: *2009*

### Describe in Detail

Essay▾Describe the procedure of drawing a simple random sample of size n without replacement from a finite population of size N. obtain the probabilities of drawing specified sample in simple random sampling with and without replacement.

### Explanation

Procedure of drawing Simple random sampling without replacement (SRSWOR) :

In SSWOR once an element is selected as a sample unit, it will not be replaced in the population pool. The selected sample units are distinct.

A sample of size is collected without replacement from the population of size . First member is chosen at random from the population,…

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## Question 25

## Question 26

Appeared in Year: *2009*

### Write in Short

Short Answer▾Describe the Yule -Slutsky effect of moving average operation on the random component of a time series.

## Question 27

Appeared in Year: *2009*

### Describe in Detail

Essay▾Distinguish between two-stage and two-phase sampling schemes. Give suitable examples.

### Explanation

Two Stage Sampling:

All elements are surveyed in cluster sampling and efficiency in cluster sampling depends on size of the cluster. As the size increases, the efficiency decreases.

Rather than enumerating all the sampling units in the selected clusters, one can get better and more efficient estimators by resorting to sub sampling within the clusters…

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## Question 28

Appeared in Year: *2009*

### Describe in Detail

Essay▾Define multicollinearity. What are the causes of multicollinearity? How will you detect the same and solve it?

### Explanation

**Multicollinearity**: Implies predictors that are correlated with other predictors in the model. Here two or more predictor variables in a multiple regression model are highly correlated and implies that one can be linearly predicted from the others with a substantial degree of accuracy.

**Causes of multicollinearity**:

- Inaccurate use of dummy variables.
- Inc…

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## Question 29

Appeared in Year: *2010*

### Describe in Detail

Essay▾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 30

Appeared in Year: *2011*

### Describe in Detail

Essay▾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 31

Appeared in Year: *2010*

### Write in Short

Short Answer▾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