# ISS (Statistical Services) Statistics Paper III: Questions 32 - 36 of 109

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## Question 32

Appeared in Year: *2011*

### Write in Short

Short Answer▾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 33

Appeared in Year: *2010*

### Describe in Detail

Essay▾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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## Question 34

Appeared in Year: *2010*

### Describe in Detail

Essay▾What is cluster sampling? In the case of cluster sampling for proportions, obtain an unbiased

Estimator of population proportion. Also, compute variance of your estimator.

### Explanation

**Cluster sampling**:

Cluster sampling is a type of sampling method. In this method, the population is divided into separate groups, called clusters. Then, a simple random sample of clusters is selected from the population. Then analysis is done on the data from the obtained sampled clusters.

The samplings lead to several difficulties if the population s…

… (219 more words) …

## Question 35

Appeared in Year: *2011*

### Write in Short

Short Answer▾**Explain the concept of simple random/sampling with and without replacement. In a simple Random sampling, show that is an unbiased estimator of **.

## Question 36

Appeared in Year: *2011*

### Describe in Detail

Essay▾Explain the errors in the measurement of price and quantity index number.

### Explanation

All index numbers are affected by mainly three types of errors.

- Formula error
- Sampling error
- Homogeneity error
Formula error:

There is no universally accepted index number formula that will measure the price or quantity changes excatly. Each formula in common use has its own defeat and consequently some error is natural in all index number formula. This…

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