# ISS (Statistical Services) Statistics Paper III: Questions 66 - 73 of 96

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## Question number: 66

» Applied Statistics » Index Numbers » Laspeyre

Appeared in Year: 2013

### Describe in Detail

Why do the errors occur in the measurement of price and quantity index numbers? Give the names of those errors.

### Explanation

**Errors in the measurement of price and quantity index numbers: **

Generally, index numbers for prices are constructed from *m* commodities, which are common to both the base year and the given year. But in practical calculations, it may not be possible to consider all common commodities say, M.

Therefore,

## Question number: 67

» Sampling Techniques » Probability Sampling or Random Sampling

Appeared in Year: 2012

### Write in Short

Let be the *y*-value of the i^{th} unit and be corresponding selection probability,

i = 1, 2, …, N. Then, based on a sample of size n drawn with replacement, show that an unbiased estimator for population total is

## Question number: 68

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

Appeared in Year: 2013

### Describe in Detail

Explain the following:

(i) Weighted Aggregates method

(ii) Criteria of a good index number

### Explanation

** (i) Weighted Aggregates Method: **

In this method, an index number of prices for any given year is calculated after assigning the appropriate weights to the different items included in that index number.

Usually weights are assigned on the basis of quantities, values or sale price of the commodities consumed during

## Question number: 69

» Econometrics » Prediction and Simultaneous Confidence Intervals

Appeared in Year: 2012

### Write in Short

Discuss forecasting accuracy and Theil’s U coefficient.

## Question number: 70

» Applied Statistics » Index Numbers » Income Distribution-Pareto and Engel Curves

Appeared in Year: 2012

### Write in Short

Using curves of concentration, discuss the formulation of the problem of distribution of income.

## Question number: 71

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2012

### Write in Short

Obtain the general solution of first-order auto-regression model.

## Question number: 72

» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process

Appeared in Year: 2013

### Describe in Detail

Discuss the relevance of variate difference method in time series analysis data. Show that

### Explanation

**Relevance of variate difference method: **

Although many different formulas are used to measure the random component in a time series, , the variate difference method fits the best, because this method method enables us to estimate the variance of the random component in a series. The variate difference method does

## Question number: 73

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2013

### Describe in Detail

Explain circular systematic sampling. Show that minimum value of ρ is** , **when **, **where ρis intraclass correlation and** **is the sample mean.

### Explanation

**Circular systematic sampling**

This method consists of choosing a random start from 1 to N and selecting the unit corresponding to the random start and thereafter every k^{th} unit in a cyclic manner till a sample of size n units is obtained, k being the integer nearest to