ISS (Statistical Services) Statistics Paper III: Questions 37 - 42 of 109
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Question 37
Appeared in Year: 2011
Describe in Detail
Essay▾Let for a stratified random sampling where is constant, is the-cost per unit-in ith 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
Appeared in Year: 2011
Describe in Detail
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
… (22 more words) …
Question 39
Appeared in Year: 2011
Describe in Detail
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…
… (128 more words) …
Question 40
Appeared in Year: 2011
Describe in Detail
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…
… (232 more words) …
Question 41
Appeared in Year: 2010
Write in Short
Short Answer▾Discuss briefly the steps involved in the construction of cost of living index number.
Question 42
Appeared in Year: 2010
Write in Short
Short Answer▾Discuss the ratio to trend method for separating the seasonal component in a time series.