ISS (Statistical Services) Statistics Paper III: Questions 62 - 68 of 96
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Question number: 62
» Applied Statistics » Index Numbers » Income Distribution-Pareto and Engel Curves
Appeared in Year: 2012
Write in Short
Discuss Engel’s law and Engel’s curve. Explain Engel ’s curve for constant price.
Question number: 63
» Sampling Techniques » Stratified Random Sampling
Appeared in Year: 2012
Describe in Detail
Discuss the allocation of a sample to different strata in stratified sampling. Explain proportional allocation and hence obtain the variance of mean of a stratified sample under proportional allocation.
Explanation
For a population consisting of N sampling units it can be divided into k relatively homogeneous sub-groups of sizes, , …, (called as strata) such that N=.
Then a simple random sample of size (i = 1,2, …, k) is drawn from each of the stratum such that n=, and this sample is the stratified random sample of size n.
Allocati
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Question number: 64
» Sampling Techniques » Simple Random Sampling With and Without Replacement
Appeared in Year: 2012
Write in Short
Show that for a simple random sample unbiased estimate of
Question number: 65
» Econometrics » Ordinary Least Squares (OLS)
Appeared in Year: 2012
Write in Short
If the demand curve is of the form , where p is the price and x is the demand, prove that the elasticity of demand is · Hence deduce the elasticity of demand for
Question number: 66
» Applied Statistics » Index Numbers » Laspeyre
Appeared in Year: 2013
Describe in Detail
Why do the errors occur in the measurement of price and quantity index numbers? Give the names of those errors.
Explanation
Errors in the measurement of price and quantity index numbers:
Generally, index numbers for prices are constructed from m commodities, which are common to both the base year and the given year. But in practical calculations, it may not be possible to consider all common commodities say, M.
Therefore, value index can be either in terms of
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Question number: 67
» Sampling Techniques » Probability Sampling or Random Sampling
Appeared in Year: 2012
Write in Short
Let be the y-value of the ith unit and be corresponding selection probability,
i = 1,2, …, N. Then, based on a sample of size n drawn with replacement, show that an unbiased estimator for population total is
Question number: 68
» Applied Statistics » Index Numbers » Price Relatives and Quantity or Volume Relatives
Appeared in Year: 2013
Describe in Detail
Explain the following:
(i) Weighted Aggregates method
(ii) Criteria of a good index number
Explanation
(i) Weighted Aggregates Method:
In this method, an index number of prices for any given year is calculated after assigning the appropriate weights to the different items included in that index number.
Usually weights are assigned on the basis of quantities, values or sale price of the commodities consumed during the base year or in some typical
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