# ISS (Statistical Services) Statistics Paper III: Questions 37 - 41 of 109

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## Question number: 37

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

Let for a stratified random samplingwhereis 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 (

… (155 more words) …

## Question number: 38

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

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

… (125 more words) …

## Question number: 39

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

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:

1. OLS estimators will be BLUE, but they have large variances and covariances. this makes the estimation difficult.

2. 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

… (160 more words) …

## Question number: 40

» Applied Statistics » Time Series Analysis » Exponential and Moving Average Smoothing

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

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 averag

… (234 more words) …

## Question number: 41

» Applied Statistics » Index Numbers » Price Relatives and Quantity or Volume Relatives

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Appeared in Year: 2010