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

**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.