Title STATS.pdf ✅

Page | 1 MODEL PAPER - 2022 II PUC SUBJECT: STATISTICS (31) [Total No. of questions: 55] Time: 3Hrs.15Mins. Max. Marks: 100 Note: 1. Statistical table and graph sheets will be supplied on request. 2. Scientific calculators may be used. 3. All working steps should be clearly shown. Section – A I. Answer anyten of the following questions. 10 × 1 = 10 1. Define fecundity. 2. Define life table. 3. Name the index number which does not satisfy unit test. 4. Define consumer price index number. 5. What is Historigram? 6. Which variation of the time series is unpredictable? 7. Write the parameter of a Bernoulli distribution. 8. What is the total area under the normal curve? 9. For a chi square  2  variate, if  13.33 0.5 2 P 0     , find median. 10. What is meant by estimation? 11. Define null hypothesis. 12. Define confidence interval. 13. What is a control chart? 14. In L.P.P define solution. 15. Define ‘strategy’ in a game. Section – B II. Answer anyten of the following questions. 10 × 2 = 20 16. Mention two uses of vital statistics. 17. In a life table, if l1 = 95,400 and l2 = 93,492 then, find d1. 18. Mention two characteristics of index numbers. 19. If p1q = 450 and p0q= 400, find Kelly’s price index number. 20. Find consumer price index number from the following data. Group A B C D Group Index 100 120 130 110 Weight 2 3 1 4 21. Mention two uses of time series. 22. Diagrammatically represent ‘Business Cycle’ with stages. 23. Write down the conditions for applying of Binomial expansion method of interpolation and extrapolation. 24. Find P(X = 0) in a Poisson distribution with mean 5. 25. If n = 4 for student’s t-distribution, find S.D. 26. If P = 0.1 and n = 100, then find S.E(p). 27. Define type I and type II errors.
Page | 2 28. If X = 40, R =2.5 and A2= 0.577, find lower control limit of X- chart. 29. What are degenerate and non-degenerate solutions in T.P? 30. Mention two needs for replacement of equipments. Section – C III. Answer any eight of the following questions. 8 × 5 = 40 31. From the following data, find CBR and GFR. Age [in years] Male Population Female Population Number of live births 0 - 14 46000 43000 - 15 - 24 34000 32000 6846 25 - 39 39000 38000 3893 40 - 49 30000 28000 674 50 - 79 27000 26000 - 80 & above 15000 12000 - 32. For the following data, calculate gross reproduction rate. Age group [in years] 15 - 19 20 - 24 25 - 29 30 - 34 35 - 39 40 - 44 45 - 49 Female population 14,000 15,000 14,000 13,000 12,000 11,000 10,000 Female births 630 870 980 650 600 220 30 33. What are the steps involved in the construction of index number? Explain any two of them. 34. The following are the prices (in Rs.) of items in 2010 and 2015. Find simple geometric mean price index number. Item A B C D E F Price 2010 50 60 20 50 80 125 (Rs.) 2015 55 75 30 75 70 130 35. Obtain trend values by 3 yearly moving averages for the following data. Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Sales (‘000) 86 63 45 58 43 57 98 120 100 150 36. For the following time series fit a linear trend by the method of least squares. Year 2002 2004 2006 2008 2010 2012 Profit (in crores) 10 20 32 36 52 60 37. Interpolate and extrapolate the production for the years 2000 and 2010 with the help of the following table. Year 1980 1985 1990 1995 2000 2005 2010 Production (tons) 5 12 19 26 - 40 -
Page | 3 38. In a city 40% of the people are vegetarians. In a random sample of 6 persons find the probability that i) 3 are vegetarians, ii) at least one is vegetarian. 39. A pond has 10 fishes among which 4 are marked ones (marked fishes are under scientific observation). 4 fishes are caught from the pond. Find the probability that two of them are marked ones. Also find the mean of marked ones. 40. It is required to test whether those who practice Yoga have average blood sugar less than 120 mg/dl. A sample consisting of 36 persons who practice Yoga is observed. If their mean blood sugar is 118.5 mg/dl and variance is 9 mg2/dl. At 1% level of significance what would you conclude? 41. For the following data examine whether the means differ significantly? Use α=0.05. Sample I II Size 12 7 Mean 57.2 52.3 S.D. 3.41 3.62 42. From the following data, test whether ‘education’ and ‘employment’ are independent at 1% level of significance. Education Employment Employed Unemployed Educated 20 25 Uneducated 15 40 43. In a floor mat manufacturing company, the average number of defects per square meter is known to be 4. Determine the control limits for the number of defects. 44. Solve the following L.P.P graphically: Max. Z = 10x + 15y s.t. x + y ≤ 10 3x + 2y ≥ 15 and x, y ≥ 0 OR (For visually challenged students only) Explain graphical method of solving L.P.P. 45. Solve the following game using the principle of dominance.
Page | 4 4 1 2 3 1 2 3 Player B B B B B A Player A A A 1 2 0 3 4 6 3 5 3 1 2 0           Section – D IV. Answer any two of the following questions. 2 × 10 = 20 46. From the following data, compute standardized death rates for Town A and Town B. Comment on the results. Age group [in years] Town - A Town - B Standard Population Deaths Population Deaths Population 0 – 20 4,000 36 3,000 30 2,000 20 – 40 12,000 48 20,000 100 3,000 40 – 60 6,000 60 4,000 48 6,000 60 & above 8,000 152 3,000 60 4,000 47. Find Laspeyre’s, Paasche’s and Dorbish-Bowley’s price index numbers for the following data. Item 2004 2008 Price (Rs.) Quantity Price (Rs.) Quantity A 10 5 15 4 B 15 8 20 7 C 6 3 10 5 D 3 4 4 5 48. For the following data verify whether Fisher’s index number satisfies TRT and FRT. Item Price (Rs.) Quantity Base year Current year Base year Current year A 4 6 4 6 B 6 10 4 8 C 8 11 5 3 49. For the following time series fit a second degree trend of the type Y = a + bx + cx2 by the method of least squares. Estimate the profit for the year 2010. Year 2005 2006 2007 2008 2009 Profit (in lakhs) 10 8 12 18 26 50. Following is the data regarding number of mistakes per page found in a book. Fit a Poisson distribution. Test at 5% L.O.S. that it is a good fit. No. of mistakes per page 0 1 2 3 4 5 and more No. of pages 31 34 21 12 2 0 Section – E V. Answer any two of the following questions. 2 × 5 = 10
Page | 5 51. Marks scored by the students of a class follows normal distribution with mean 80 and S.D. 5. Find the probability that a student selected at random from the class scored i) more than 70 marks ii) between 75 and 90 marks. 52. In a random sample of 120 people from a city in the year 2011 revealed that 96 were cricket match viewers. In another random sample of 100 people from same city in the year 2013 revealed that 90 were cricket match viewers. Examine whether there is a significant increase in the proportion of cricket match viewers. Use 1% level of significance. 53. The following data represents the blood pressure of 5 persons before and after performing dhyana: Person A B C D E B.P. Before Dhyana 90 90 100 88 99 B.P. After Dhyana 88 90 95 90 96 Can we conclude at 5% level of significance that Dhyana reduces blood pressure? 54. The purchase price of a machine is Rs 8,000. Its maintenance costs and resale values are given below: Year 1 2 3 4 5 Maintenance cost (Rs.) 500 600 800 1,100 1,500 Resale value (Rs.) 4,500 3,500 2,500 1,500 500 What would be the optimum replacement period of machine? What would be the average annual cost? 55. There is a demand for 10,000 items per year. The replenishment cost is Rs.200 and the maintenance cost is Rs.9 per item per year. Replenishment is instantaneous and shortages are not allowed. Find economic order quantity and minimum average inventory cost. *****