Sample Question Paper Statistics Karnataka : Pre University / PU www.pue.kar.nic.in

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Document Described : Statistics Question Paper, Karnataka Question Paper

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.

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SECTION – A :
I. Answer the following questions : 10 × 1 = 10
1. In a life table define ‘Radix’.
2. What is the value of Index number for the base year ?
3. State the relation between Laspeyre’s, Paasche’s and Fisher’s Indices.
4. What is meant by trend ?
5. For what value of ‘p’ is Binomial distribution symmetrical ?
6. Write down the probability function of a normal variate which has mean 8 and variance 9.
7. Define Statistical Hypothesis.
8. In a chi square test for goodness of fit if there are 8 classes and if two parameters are estimated, what is the degrees of freedom of the test statistic ?
9. When do you call a game unfair ?
10. Give one use of statistical quality control.

SECTION – B :
II. Answer any ten of the following questions : 10 × 2 = 20
11. Give any two comparisons between CDR and STDR.
12. If Laspeyre’s index is 137·1 and Paasche’s index is 139·3, find Dorbish-Bowley index.
13. Define consumer price index number.
16. Find P ( X = 0 ) in a Poisson distribution with mean 5.
17. Define Type I and Type II errors.
18. A random sample of size 36 is drawn from a population whose
variance is 16. Write down the standard error of the sample mean.
20. Specify two needs for replacement of capital equipment.
21. Write two advantages of maintaining an inventory.
22. Mention the UCL and LCL in C-chart when standards are unknown.

SECTION – C :
III. Answer any eight of the following questions : 8 × 5 = 40
23. From the following data calculate the CBR, GFR and ASFR for the age
group ( 25 - 39 ) :
Age group ( in year ) Male population Female population Births occurring to females
0 — 14 46,000 43,000 —
15 — 24 34,000 35,000 6,846
25 — 39 39,000 38,000 3,893
40 — 49 30,000 28,000 674
50 — 79 27,000 26,000 —
80 & above 3,000 4,000 —
24. From the following data compute a suitable price index number:
Commodity Price Quantity
1970 1980 1980
A 20 40 6
B 50 60 5
C 40 50 15
D 20 20 25
Code No. 31 16
25. Calculate the cost of living index number from the following data :
Items Price Weights
Base Year Current Year
Food 30 47 4
Fuel 8 12 1
Clothing 14 18 3
House rent 22 15 2
Miscellaneous 25 30 1
26. Compute four yearly moving averages for the following data :
Year 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979
Sale 75 60 55 60 65 70 70 75 85 70
28. If a random variable X follows Poisson distribution such that P ( X = 1 ) = P ( X = 2 ), find —
a) the mean and standard deviation of the distribution
b) P ( X = 0 )
29. In a sample of 500 people in Kerala 280 are tea drinkers and the rest
are coffee drinkers. Can we assume that both coffee and tea are
equally popular in this state at 1% level of significance ?
31. The mean weekly sales of the chocolate bar in candy stores were 146·3 bars. After an advertising campaign the mean weekly sales in 22 stores for a typical week increased to 153·7 bars and showed standard deviation of 17·2. Was the advertisement campaign successful ?
32. Graphically solve the following :
Maximize Z = 100x + 20y
Subject to x + 2y = 20
2x + 5y = 80
and x = 0, y = 0
33. A taxi owner from his past records finds that the maintenance cost
per year of a taxi whose purchase price is Rs. 8,000 are as given
below :
Years Maintenance Cost ( Rs. ) Resale Value ( in Rs. )
1 1,000 4,000
2 1,300 2,000
3 1,700 1,200
4 2,200 600
5 2,900 500
6 3,800 400
7 4,800 400
8 6,000 400
Determine when it is profitable to replace the taxi.
Code No. 31 16
34. 10 samples each of size 5 were inspected and the number of
defectives in each of them were as follows:
Sample number 1 2 3 4 5 6 7 8 9 10
Number of defectives 0 2 3 1 2 3 0 1 2 1
Get the control limits for number of defectives ( np-chart ).

SECTION – D :
IV. Answer any two of the following questions : 2 × 10 = 20
35. a) Compute standardized death rates for towns X and Y and state which town is healthier:
Age ( in Yrs. ) Town X Town Y Standard Population Population Death per 1000 Population Death per 1000
0 — 9 13,500 10 8,700 12 35,000
10 — 29 8,900 18 5,500 20 15,000
30 — 59 5,000 20 3,700 24 20,000
60 & above 12,000 15 6,900 18 30,000

b) From the following data calculate TFR :
Age group ( in years ) Female population No. of births occurring to females
15 — 19 8,943 271
20 — 24 8,356 1,343
25 — 29 8,431 1,492
30 — 34 8,013 1,026
35 — 39 7,962 731
40 — 44 7,346 182
45 — 49 6,700 42

36. Compute Fisher’s price index on the basis of the following data :
Commodity Base Year Current Year
Price Expenditure Price Expenditure
A 5 25 10 60
B 1 10 2 24
C 4 16 8 40
D 2 40 5 75
Also apply TRT and FRT to the above index number.
37. Production figures of a sugar factory in 1000 quintals are given
below:
Year 1970 1971 1972 1973 1974 1975 1976
Production 12 10 14 11 13 15 16
a) Fit a straight line trend to the above data
b) Plot these figures on a graph and show the trend line
c) Estimate the production for 1979.
38. Records taken of the number of male births in 800 families having
four children are given below :
Male births: 0 1 2 3 4
No. of families : 32 178 290 236 64
Test the hypothesis that male & female births are equally likely at 5%
level of significance.

SECTION – E :
V. Answer any two of the following questions : 2 × 5 = 10
39. The weekly wages of workmen are normally distributed around a mean of Rs. 70 and with a standard deviation of Rs. 5. Find the probability of workers whose weekly wages will be
a) more than Rs. 80
b) between Rs. 69 and Rs. 72.
40. 400 women shoppers are chosen at random in market A. Their average weekly expenditure on food is found to be Rs. 250 with a s.d. of Rs. 40. The figures are Rs. 220 and Rs. 55 respectively in the market B, where also 400 women shoppers are chosen at random. Test at 1% level of significance whether the average weekly food expenditures of populations of shoppers are equal.
41. A milk filling machine fills sachets with milk. The contention is that standard deviation of quantity of milk filled is more than 3 ml. To test this 24 sachets are randomly selected and their content noted. If the standard deviation of these observations is 3·8 ml, what is your conclusion ?
42. Two players A and B play a game A writes either red or blue or green on a piece of paper. He hides that he has written from his opponent. Player B without knowing what A has written should guess it. If his guess is correct, A should pay Rs. 100 to B, otherwise B should pay Rs. 60 to A. Write down the pay-off matrix of A. Does the game have a saddle point ?

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Why should a feasible region lie in the first quadrant?