1. Distinguish between the Ratio to Trend. Method and Ratio to Moving Average Method for the measurement of seasonal variations.

2. What is Systematic Random Sampling What are its advantages and disadvantages? How is it different from Simple Random Sampling?

Differentiate between Coefficient of Variation and Concentration Ratio. What is Lorenz curve?

During April 2009, the daily closing of ABCD, WXY and Z-Corp was the following:

ABCD WXY Z-Corp
Mean closing values April 2009 134·4 179·5 98·6
Standard deviation of closing values for July 1999 2·6 3·77 3.72

For each stock, compute the coefficient of variation. Comment on the results from each stock.

Explain the method of least squares in determining trend.

The sales of a company (in thousands of Rs) for the years 2004 to 2010 are shown below:

Year Sales

2004 32

2005 47

2006 65

2007 92

2008 132

2009 190

2010 275

Fit an exponential trend A.B^X) and estimate the sales for 2011.

On a final examination in Mathematics, the mean was 72 and the standard deviation was 15. Determine the standard scores (i.e. grades in standard deviation units) of students receiving the grades 60 93.

Explain with an example, the method of testing of hypothesis for a single sample when population variance is known.

6. In a sample of 5 measurements, the diameter of a sphere was recorded by a scientist as 6·33, 6·37, 6·36,6.32 and 6·37 cm. Determine unbiased and efficient estimates of

the true mean

the true variance

7. What is Poisson distribution Explain its characteristics and derive an expression to calculate the probability mass function of a Poisson distribution.

8. Explain the concept of rank correlation coefficient. Compute the rank correlation coefficient from the following data

In a drawing competition 11 candidates were judged by 2 judges and the ranks given by them were:

Rank given by A B C D E F G H I J K
Judge 1 1 4 8 6 7 1 3 2 5 10 9
Judge 2 2 3 9 6 5 1 2 4 7 8 10

9. What are the different types of Non-Probability Sampling Explain their advantages and disadvantages.

10. What is the difference between Discrete and Continuous Random Variable Derive an expression for mean and variance of a random variable.

11. The Ministry of Labour collects information on the ages of people in civilian labour force and publishes the results in Employment News. Fifty people in the civilian labour force are randomly selected and their ages.are displayed in the table below:

22 58 40 42 43

32 34 45 38 19

33 16 49 29 30

43 37 19 21 62

60 41 28 35 37

51 37 65 57 26

27 31 33 24 34

28 39 43 26 38

42 40 31 34 38

35 29 33 32 33

Find a 95% confidence interval for the mean age u of all people in the civilian labour force. Assume that the population standard deviation of the ages is 12.1 years.

12. The volume of water in commercially supplied drinking water containers is normally distributed with mean 70 litres and standard deviation 0·75 litres. Estimate the proportion of containers likely to contain the following:

In excess of 70.9 litres

At most 68·2 litres

13. An urn contains 1 red ball and 10 blue balls. Other than their colour, the balls are indistinguishable, so if one is to draw a ball from the urn without peeking, all the balls will be equally likely to be selected. If we draw 5 balls from the urn at once without peeking, what is the probability that this collection of 5 balls contains the red ball?

14. A survey publishes annual price figures for new low cost homes. The figures are obtained from sampling, not from a census. A simple random sample of 36 new low cost homes yielded the prices (in thousands of RS) as shown in the table below. Use the data to determine the population mean price u of all new homes:

67·8 68·4 59·2 56·9 63·9 62·2 55·6 72·9 62.6
67·1 73·4 63·7 57.7 66·7 61·7 55.5 49·3 72·9
49·9 56.5 71·2 59.1 64·3 64.0 55·9 51·3 53·7
56·0 76·7 76·8 60·6 74·5 57·9 70·4 63.8 77·9