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


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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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