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

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## Question number: 33

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2010

### 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

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## Question number: 34

» Sampling Techniques » Cluster Sampling With SRS - Intra-Class Correlation Coefficient

Appeared in Year: 2010

### 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

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## Question number: 35

» Sampling Techniques » Simple Random Sampling With and Without Replacement

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

### Describe in Detail

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

### Explanation

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## Question number: 37

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2011

### Describe in Detail

Let for a stratified random samplingwhereis constant, is the-cost per unit-in i^{th }stratum**, ** is the mean square based on** **units.

Estimate the sample sizen under optimum allocation for fixed cost**. **

### Explanation

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## Question number: 38

» Econometrics » Ordinary Least Squares (OLS)

Appeared in Year: 2011

### 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

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