# ISS (Statistical Services) Statistics Paper III: Questions 7 - 11 of 109

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## Question 7

Appeared in Year: *2015*

### Describe in Detail

Essay▾In the construction of price index numbers, explain the terms ‘time reversal test’ and ‘factor reversal test’ . Show that both these tests are satisfied by the Fisher index.

### Explanation

Price index numbers which measure the change in the retail or wholesale prices of a commodity at current period to some previous period. In the construction of price index numbers various test is consider tom find the accuracy of the formula. We explain the following test.

__(i) Time reversal test__: An index formula would be accurate if it maintains ti…

… (239 more words) …

## Question 8

Appeared in Year: *2015*

### Write in Short

Short Answer▾State the problem of autocorrelation in a general linear model. Why does this problem arise? Demonstrate its effect on ordinary least square estimator (OLSE) .

## Question 9

Appeared in Year: *2015*

### Describe in Detail

Essay▾Show that SRSWOR, the sample proportion is an unbiased estimator of the population proportion of members possessing a certain character. Hence obtain the variance of the estimator.

### Explanation

If we are interested in estimating the proportion of a certain character, the population of N fields can be defined with variate y_{i} as having value 1 if the field is particular characteristic, otherwise zero. If the total number of particular characteristic be N_{1} out of N

Thus,

The problem of estimating a population proportion becomes that of estimat…

… (79 more words) …

## Question 10

Appeared in Year: *2015*

### Describe in Detail

Essay▾Write down the auto correlation function of order k. For an AR (1) model X_{t} = 0.7X_{t-1} + ϵ_{t} , where {ϵ_{t}} is a white noise process. Show that this model can be expressed as a moving average process of infinite order. Check the model of stationary.

### Explanation

Autocorrelations are measures of dependence between variables in a time series. Suppose that Y_{1} , Y_{2} , … , Y_{n} are square integrable random variables with the property that the covariance

of observations with lag k does not depend on t. Then

is called the auto covariance function and

is called the autocorrelation function.

For an AR (1) model

where {ϵ_{t}} …

… (94 more words) …

## Question 11

Appeared in Year: *2015*

### Describe in Detail

Essay▾The following information concerns changes in price and consumption (quantity) of certain major of components of the consumption basket of the labour class:

- | - | - | Year 2000 | Year 2000 | Year 2014 | Year 2014 |

SI. No. | Item | Unit | Price (₹) | Consumption | Price (₹) | Consumption |

1 | Rice | Quintal | 500 | 16 | 640 | 20 |

2 | Wheat | Quintal | 240 | 52 | 320 | 10 |

3 | Cloth | Metre | 16 | 50 | 20 | 35 |

Compute price index using

(i) Fisher՚s method

(ii) Marshall-Edgeworth method

Also interpret the results.

### Explanation

To compute price index, various index methods is consider. Here for this portfolio we consider two index methods.

Where

And

So, we find the value by given table assumes base period is 2000.

- | - | - | Year 2000 | Year 2000 | Year 2014 | Year 2014 | p_{0} q_{0} | p_{t} q_{0} | p_{0} q_{t} | p_{t} q_{t} |

… (117 more words) …