# ISS (Statistical Services) Statistics Paper III: Questions 12 - 16 of 96

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## Question number: 12

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2015

### Describe in Detail

What are the advantages of stratified sampling? Consider the allocation of sample size n _{i} of strata given by , where N _{i} is the stratum size, σ _{i} is the within stratum standard deviation of the ith stratum, (i = 1, 2, …, k) and δ real. Write down the expression for the where stands for the unbiased estimator of the population mean of the study variate y based on sample random sample without replacement in each stratum.

### Explanation

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## Question number: 13

» Econometrics » Ordinary Least Squares (OLS)

Appeared in Year: 2015

### Describe in Detail

Describe in detail Indirect Least square method for estimating structural parameters. Is the estimator unbiased and/or consistent?

### Explanation

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## Question number: 14

» Econometrics » Auto-Correlation

Appeared in Year: 2015

### Describe in Detail

Describe exact and near multicollinearity in a regression model. Discuss, along with justification, the effect of these situations on (i) sampling variation and (ii) prediction.

### Explanation

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## Question number: 15

» Applied Statistics » Index Numbers » Link and Chain Relatives Composition of Index Numbers

Appeared in Year: 2009

### Write in Short

Explain the time reversal and factor-reversal tests for an ideal index number. Give an example

of index number which satisfies both of these tests.

## Question number: 16

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

Appeared in Year: 2009

### Describe in Detail

State the probability density function of the Pareto distribution and give its cumulative form.

Interpret the constants involved.

### Explanation

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