ISS (Statistical Services) Statistics Paper III: Questions 66 - 73 of 109
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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
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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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Question number: 69
» Econometrics » Prediction and Simultaneous Confidence Intervals
Appeared in Year: 2012
Write in Short
Discuss forecasting accuracy and Theil’s U coefficient.
Question number: 70
» Applied Statistics » Index Numbers » Income Distribution-Pareto and Engel Curves
Appeared in Year: 2012
Write in Short
Using curves of concentration, discuss the formulation of the problem of distribution of income.
Question number: 71
» Econometrics » Autoregressive Linear Regression
Appeared in Year: 2012
Write in Short
Obtain the general solution of first-order auto-regression model.
Question number: 72
» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process
Appeared in Year: 2013
Describe in Detail
Discuss the relevance of variate difference method in time series analysis data. Show that
Explanation
Relevance of variate difference method:
Although many different formulas are used to measure the random component in a time series, , the variate difference method fits the best, because this method method enables us to estimate the variance of the random component in a series. The variate difference method does not require the specification of a
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Question number: 73
» Sampling Techniques » Simple Random Sampling and Systematic Sampling
Appeared in Year: 2013
Describe in Detail
Explain circular systematic sampling. Show that minimum value of ρ is , when , where ρis intraclass correlation and is the sample mean.
Explanation
Circular systematic sampling
This method consists of choosing a random start from 1 to N and selecting the unit corresponding to the random start and thereafter every kth unit in a cyclic manner till a sample of size n units is obtained, k being the integer nearest to .
That is, if r is the number selected at random from 1 to N, the
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