ISS (Statistical Services) Statistics Paper III: Questions 37 - 42 of 109

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Question 37

Sampling Techniques

Stratified Random Sampling

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Appeared in Year: 2011

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Essay▾

Let for a stratified random sampling where is 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

Under optimum allocation, are obtained such that

(i) minimize the variance of the estimate for (a) fixed sample size n;

(i) var ( is minimum for fixed n

(ii) var ( is minimum for fixed total cost C

(iii) Total cost C is minimum for fixed value of var (

And the cost function C in stratified sampling is given by the linear model

Where a is the overhead c…

… (114 more words) …

Question 38

Econometrics

Ordinary Least Squares (OLS)

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Appeared in Year: 2011

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Essay▾

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

For consumer՚s equilibrium, we have

and hence, we get

⇾

⇾ … (i)

since, µ the individual income is fixed, we have

⇾

Substituting the value of in (i) , we get

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Question 39

Econometrics

Auto-Correlation

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Appeared in Year: 2011

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Essay▾

Discuss the effect of imperfect multicollinearity on tests and errors. Consider a model

with

and with

, ,

and

Do you think multicollinearity is present in the model? If yes, give reasons. Further show that as

increases, also increases .

Explanation

Effect of imperfect multicollinearity on tests and errors:

OLS estimators will be BLUE, but they have large variances and covariances. this makes the estimation difficult.
The confidence intervals will be wider. and hence, we may not reject the ′ zero null hypothesis i.e.. , We may conclude that B ′ s are not significantly different from zero even th…

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Question 40

Applied Statistics

Time Series Analysis

Exponential and Moving Average Smoothing

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Appeared in Year: 2011

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Essay▾

Explain moving average [m, p] . Let with p = 1 and m = 2k + 1, obtain the coefficient of and [m, p]

Explanation

Moving average: moving average method is a simple and flexible method for measuring trend. It consists in measurement of trend by smoothing out the fluctuations of the data by means of a moving average.

The first element of the moving average is obtained by taking the average of the initial fixed subset of the number series i.e.. the first average i…

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