Code No. 31
March, 2009 STATISTICS
Time : 3 Hours 15 Minutes ] [ Max. Marks : 100
Note : i) Statistical tables will be supplied on request. ii) Scientific calculators may be used. iii) All working steps should be clearly shown.
SECTION – A
I. Answer the following questions : 10 × 1 = 10
1. Which measure should be used for comparing health conditions of two towns ? 2. Theoretically which best average is used in the construction of index numbers ? 3. Which weights are used in the construction of Paasche's price index number ? 4. Mention any one of the factors causing seasonal variations. 5. For a Binomial distribution mean = 7 and variance =11. Is the above statement correct ? 6. For the application of χ 2 distribution, what is the condition for expected cell frequency ? 7. Define Standard Error. 8. Which is the best estimator of the population mean ? 9. What is the principle adopted for replacement of equipment which deteriorate with age ? 10. SQC helps in detecting which type of variation ?
SECTION – B
II. Answer any ten of the following questions : 10 × 2 = 20
11. The Quinquennial ASFRs for women of child bearing age of a community are 26, 63, 65, 46, 24, 13 & 7. Compute TFR.Code No. 31 10 12. If price of a commodity is Rs. 10 in 2002 and Rs. 35 in 2008, then compute the index number of price. 13. Why Fisher's index number is called an 'Ideal' ? 14. Which components of a time series are associated with the following sentences ? a) Fall in death rate due to advance in science. b) An increase in employment during harvest season. 15. In a Poisson distribution the first probability term is 0·2725. Find the next probability term. 16. The distribution of a variable X is given by the law f ( x ) = 15 2πe– 12 ( ) X – 1005 2. Write down the values of mean and standard deviation. 17. Define onetailed and twotailed tests. 18. The proportion of vegetarians in a city is 0·48. Find the standard error of the proportion of vegetarians in a random sample of size 20. 19. Write down the ttest statistic and degrees of freedom in the case of test for equality of means. 20. In an LPP define optimal solution. 21. In a rectangular game payoff matrix of Player A is B 1 B 2 B 3 B 4 A 1 5 3 8 – 6 A 2 5 10 – 3 – 6 Write down the payoff matrix of Player B. 22. What is a Control Chart ? Name the control chart for variables.11 Code No. 31
SECTION – C
III. Answer any eight of the following questions : 8 × 5 = 40
23. Taking Town A as standard, find the STDRs & comment. Age Population ASDR Groups Town A Town B Town A Town B 0 – 20 4,000 3,000 7·5 10 20 – 40 12,000 20,000 3·33 5 40 – 60 6,000 4,000 10 10 60 & above 8,000 3,000 8·75 20 24. For the following data verify whether Fisher's index number satisfies FRT : 2000 2005 Commodities Price ( Rs. ) Value Price ( Rs. ) Value A 4 40 5 50 B 3 21 3 27 C 6 48 8 40 D 5 30 4 32 25. Construct a suitable consumer price index number for the folowing data : Group Base Year price ( Rs. ) Current Year price ( Rs. ) Base Year expenditure Food 120 160 600 Clothing 40 60 320 Fuel & Lighting 80 100 800 Entertainment 20 40 500 Medicine & Education 30 60 450 Miscellaneous 45 80 1,350Code No. 31 12 26. Estimate the trend values using the data given below by taking four yearly moving averages : Year Values 1994 12 1995 25 1996 39 1997 54 1998 70 1999 87 2000 105 2001 100 2002 82 2003 65 27. If on an average 1 ship in every 10 is sunk, find the chance that out of 5 ships expected at least 4 will arrive safely. 28. In a certain factory turning out optical lenses there is a small chance 1/500 for any one lens to be defective. The lens are supplied in packets of 10. Use Poisson distribution to calculate the approximate number of packets containing one defective lens in a consignment of 20,000 packets. 29. 490 male students and 450 female students appeared at an examination in commerce. The mean and S.D. in marks of male students are 54·3 and 17·5 respectively, whereas those of female students are 50·6 and 18·0. Is there a significant difference in marks of male and female students ?13 Code No. 31 30. A tobacco company claims that there is no relationship between smoking and lung ailments. To investigate the claim a random sample of 300 males in the age group of 40 to 50 are given medical tests. The observed sample results are tabulated below : Ailment Smoking Lung ailment No Lung ailment Smokers 75 105 Nonsmokers 25 95 On the basis of this information can it be concluded that smoking and lung ailment are independent ? 31. An IQ test was administered to 5 persons before and after they were trained. The results are given below : Candidates : I II III IV V IQ before training : 110 120 123 132 125 IQ after training : 120 118 125 136 121 Test whether there is any change in IQ after the training programme. 32. Solve the game by maximinminimax principle whose payoff matrix is given by Player B B 1 B 2 B 3 A 1 1 3 1 Player A A 2 0 – 4 – 3 A 3 1 5 – 1Code No. 31 14 33. A truck owner from his past records finds that the maintenance costs per year of a truck whose purchase price is $ 8,000 are as given below : Year : 1 2 3 4 5 6 7 8 Maintenance cost ( in $ ) 1,000 1,300 1,700 2,200 2,900 3,800 4,800 6,000 Resale price ( in $ ) 4,000 2,000 1,200 600 500 400 400 400 Determine at which time it is profitable to replace the truck. 34. Twenty pieces of cloth out of different rolls contained respectively 1, 4, 3, 2, 5, 4, 6, 7, 2, 3, 2, 5, 7, 6, 4, 5, 2, 1, 3, 8 imperfections. Calculate control limits for suitable control chart.
SECTION – D
IV. Answer any two of the following questions : 2 × 10 = 20
35. The following table gives the age and sex distribution and the number of live births occurring in a year in a population : Age( in years )Male population Female population Live births to females 0 – 14 20,730 19,840 0 15 – 19 7,366 7,310 212 20 – 24 7,300 7,120 657 25 – 29 6,030 5,860 592 30 – 39 9,980 9,120 326 40 – 49 7,400 6,910 81 50 & above 8,400 7,900 0 Compute CBR, GFR & ASFRs.15 Code No. 31 36. It is stated that MarshallEdgeworth index number is a good approximation to the Fisher's Ideal index number. Verify this using the following data : Base year Current year Articles Price( Rs. ) Quantity Price( Rs. )Quantity A 10 6 15 5 B 12 10 15 10 C 18 5 27 3 D 8 5 12 4 37. Below are given the figures of production ( in thousand quintals ) of a sugar factory : Year 2001 2002 2003 2004 2005 2006 2007 Production ( in '000 qtls ) 80 90 92 83 94 99 92 a) Fit a straight line trend to these figures. b) Estimate the production for the year 2008. c) Compute the trend values. 38. The following mistakes per page were observed in a book : No. of mistakes per page No. of pages 0 211 1 90 2 19 3 5 4 0 Fit a Poisson distribution to the data and test the goodness of fit.Code No. 31 16
SECTION – E
V. Answer any two of the following questions : 2 × 5 = 10
39. X is a normal variate with mean 64 and variance 144. Determine i) P ( X ≥ 67 ) ii) P ( 60 ≤ X ≤ 66 ). 40. In a random sample of 1000 persons from town A, 400 are found to be consumers of wheat. In a sample of 800 from town B, 400 are found to be consumers of wheat. Do these data reveal a significant difference between town A and town B so far as the proportion of wheat consumers is concerned. 41. The tensile strengths of 8 rods were 8, 3, 12, 14, 7, 13, 9 and 6 tons. Test the hypothesis that the standard deviation is more than 2 tons. 42. A stockist has to supply 400 units of a product every Monday to his customers. He gets the product at Rs. 50 per unit from the manufacturer. The cost of ordering and transportation from the manufacturer is Rs. 75 per order. The cost of carrying inventory is 7·5% per year of the cost of the product. Find i) Economic lot size ii) The minimum average cost.
