# ISS (Statistical Services) Statistics Paper III: Questions 33 - 38 of 96

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## Question number: 33

Appeared in Year: 2010

Essay Question▾

### 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:

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## Question number: 34

Appeared in Year: 2010

Essay Question▾

### Describe in Detail

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 popula

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## Question number: 35

Appeared in Year: 2011

### Write in Short

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

## Question number: 36

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

Appeared in Year: 2011

Essay Question▾

### Describe in Detail

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

### Explanation

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

1. Formula error

2. Sampling error

3. 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 numb

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## Question number: 37

Appeared in Year: 2011

Essay Question▾

### Describe in Detail

Let for a stratified random samplingwhereis constant, is the-cost per unit-in ith stratum, is the mean square based on units.

Estimate the sample sizen under optimum allocation for fixed cost.

### Explanation

Under optimum allocation, are obtained such that

(i) minimize the variance of the estimate for (a) fixed sample size n;

(i) var (is minimum for fixed n

(ii) var (is minimum for fixed total cost C

(iii) Total cost C is minimum for fixed value of var (

And the cost function C in stratified sampling is given by the linea

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## Question number: 38

Appeared in Year: 2011

Essay Question▾

### Describe in Detail

If is an individual’s utility function of two goods, show that the demand for the goods is and

Where and are the fixed price and µ be the individual fixed income.

### Explanation

For consumer’s equilibrium, we have

and hence, we get

………………. (i)

since, µ the individual income is fixed, we have

Substituting the value of in (i), we get

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