ISS (Statistical Services) Statistics Paper III: Questions 60 - 65 of 96
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Question number: 60
» Applied Statistics » Index Numbers » Laspeyre
Appeared in Year: 2013
Describe in Detail
Discuss simple aggregate method of Index number. Why is weighted average of price relative index preferred over simple aggregate method? Show that weighted average of price relative index number is same as that of Paasche’s index number.
Explanation
Simple aggregate method of Index number:
This method consists of expressing aggregate of prices in any year as a percentage of their aggregate ith the base year. The price index, under this method is computed by the formula
Where
= Price index of the current year
Question number: 61
» Applied Statistics » Periodogram and Correlogram Analyses
Appeared in Year: 2012
Describe in Detail
Obtain the correlogram for the series with, provided, , and successive values of are independent.
Explanation
It is given that
And hence
Substituting the value in we get,
Where ηs are independent.
Multiplying both sides of the above equation by , taking expectations and dividing by , we get for a long series,
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
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