# 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 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

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.