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      Karnataka 2nd PUC STATISTICS (March, 2009) Question Paper


      Posted Date: 16-Aug-2010  Last Updated:   Category: Question Papers    
      Author: Member Level: Diamond    Points: 10 (Rs 1)


      Karnataka Pre University Board 2nd year STATISTICS March, 2009 Question Paper.



      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 one-tailed and two-tailed 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 t-test 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 pay-off 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 pay-off 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
      Non-smokers 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 maximin-minimax principle whose pay-off 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 Marshall-Edgeworth 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.


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