Pre University Board 2011 P.U.C. Commerce (CEBA) Statistics - Question Paper
Code No. 31
Total No. of Questions : 42 ] Total No. of Printed Pages : 16 ]
March, 2011
( Kannada and English Versions )
Time : 3 Hours 15 Minutes ] [ Max. Marks : 100
( Kannada Version )
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6. oci) &3dc!oi<), P ( - 0-8 < Z < + 0-8 ) = 0-5762 >ctii Ira&srt, P(z< + 0-8) tfoe&kssccoo.
8. H, : p. 1 < V12 &343rt H0 5?S CJdoiiO.
10. otosC rtors 3ako3,rac3<Q, V1) doid od> rbrad? sodcsoe.
II. CdJ3)CraddL0 3a STOOj : 10 X 2 = 20
11. ssfieSedfid e>0d-02Sris?) l&eodr3 sJod.w sraA &dOA>.
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12. #i ds?F\rf d;>o$rts?od &koeo wafc-d.ok dd sakcto, erodoi?A*i sSedrf dz3 .otfdcfo dodDoQcoO :
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B |
C |
D |
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102 |
97 |
108 |
110 |
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8 |
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12 |
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13. I p 0 q 0 = 382 STDrtj3 I P j q j = 424 isodi V01 30C&2oQCtoS.
14. 3>si;3s> sSrirrW acratfd <addi rfcrerts&b, sodom
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17. sjsio 3o3rtjs adFssrteto, sssjOA
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18. Pj = 0-86, P2 = 0-90, n , =40 sosrtjs n2 = 38 <aod:> &3fe3rt, >o>3 djsedrf {p \-p 2)
19. tjods 72 dcsokO n = 6 CT3 rt, ws&otf sjDrtjs azdOcSrteteb, 3odi2o8ctoQ.
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eroded. dd dd 3cood Pn. ?tadoSo8o530 : *4 CJ u 1 oi | ||||||||||||||||||
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26. #i sue; $,er3r1 5 OTdrts* riratforttf dojo3 dd sSdrts
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2 |
3 |
4 |
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7 |
8 |
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18 |
18 |
20 |
19 |
22 |
24 |
25 |
doetod ei>o ,er3r1 4 srodrte* ricraslOrte dojsotf sd sSdrttfev
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27. sodi 5(0,200 didrts?d, s&rttfi), 50 d>>3 didris?d.' srtod 4a 3d:>j3?3o><) crixra 3 dodrtsPdodo, 30 rfdoQrts ofc d, ado,
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31. s 3<od dortod. tow, &ot.Sfoo ddt> (Dskxkrt dcid rirosJO
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eorts?,, cdrad)de rtdodr d63a6?S dc&e <aodo doed.
s>cra*SO ssotfrtsfe |
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80 |
sd,o> <Ds4o?3 |
10 |
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d,&o& rra |
12 |
10 |
32. Stfrt &3&4jObd ?odd?5Deo> sidoojo? ydeO &2?i>rf>od &Aj :
rtOs| Z = 12x + 8y
S2JO$3rftk, 3x-2y < 6 x + y < 2 do, x, y > 0.
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33. & ds&od edo&F 33/d dqo&od .pa.
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34. p = 0-05 Sourt rfdojs?3 = 5 aodo Iratis/i d-ofc Scdoors odoSooDoO.
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IV. & oirasj)Cjsddf3 >tic& ero3Oft : 2 x 10 = 20
35. & Pn. sk tfockfcack, too si&otf
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sdOeloSjrfs, 3,& dc&e >ocfc> sbOedA *A t W. -t -D oOk | ||||||||||||||||||||||||||||||||||
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36. a) dso2jris?orf B sdfcracfcjck a& esdert6OTAc3d <js?Oft : 5
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& aftssroddo <adc& rtrl enOS) : 2 x 5 = 10
39. I q jp0 = 376, Zq0p0 = 350,
I Q i P i = 384, S q 0 Pj = 362 <aodo lfe3r(,
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4 |
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Note : i) Graph sheets and statistical tables will be provided on request.
ii) Scientific calculators may be used.
iii) All working steps should be clearly shown.
Answer the following questions : 10x1 = 10
1 .* What is a life table ?
2. Define Index Number.
3. Write the formula forFactor Reversal Testin Index Number.
4. Give a difference between cyclical and irregular variations in a time series,
5. Write the probability mass function of a Bernoulli distribution with range.
6. In a Normal distribution, given P (- 0-8 < Z < + 0-8 ) = 0-5762.
Find P ( Z < + 0-8 ).
7. What is Standard error ?
8. Given H,: n, < \i2, vcrite H0.
9. What is inventory. ?
10. Write a merit of acceptance sampling in Statistical quality control.
II. Answer any ten of the following questions : 10 x 2 = 20
11. Briefly explain Registration method in vital statistics.
12. Calculate consumer price index number using Family Budget method from the following data : | |||||||||||||||
|
13. Find V01 given p0 q0=382 and Qi =424.
14. Write any two merits of Least square method.
15. Mention two features of Poisson distribution.
16. In a Normal distribution, given variance is 9 cm2, find Quartile deviation.
17. Define parameter and statistic.
18. Calculate standard error (p, - p2)
Given, P, =0-86, P2 =0-90 rij =40 and n2 =38.
19. In a x2-distribution if n = 6, find Mode and Variance.
I
20. Mention two characteristics of a Competitive Game.
21. Calculate E.O.Q. given,
D = 5000 units/month Q = Rs. 10/month
C3 = Rs. 200/month.
22. Write the upper and lower control limits for X-chart, when standards are not given.
III. Answer any eight of the following questions : 8 x 5 = 40
23. Calculate Total Fertility Rate from the following data : | ||||||||||||||||||||||||||||||||||||
|
24. Explain steps involved in the construction of Consumer Price Index Number.
25. Calculate P01 by simple average of price relatives method t|sing Geometric mean from the following data ; | ||||||||||||||||||
|
26. Obtain trend values by 5 weekly moving averages method for the following time series. Plot original and trend values on a graph.
| ||||||||||||||||||||
[ ONLY FOR BLIND STUDENTS ] |
Obtain trend values using 4 weekly moving averages for the above time series.
27. In a grove there are 200 trees out of which 50 are mango trees. Among them, if 30 samples of 3 trees are selected, in how many samples will you expect
i) exactly one mango tree
ii) more than one mango tree ?
I
28. Mention any five features of Normal Curve.
29. A sample of 50 children is taken from a school. The average weight of the children is 28 kgs and standard deviation is 5 kgs. Test at 1% level of significance, if we can assume that the average weight of the school children is less than 30 kgs.
30. Students of five colleges of a certain locality participated in a match and scpred the following points :
X: 3, 5, 4, 2,1
Test at 5% level of significance the hypothesis that the population variance is more thaft 3.
31. From the following data, test if there is any significant difference between mean marks of a student in two subjects.
Statistics |
Accountancy | |
Mean marks |
84 |
80 |
Sample variance |
10 |
08 |
Sample size |
12 |
10 |
32. Solve the following Linear programming problem, graphically.
Maximise Z = 12* + 8y subejct to 3x-2y 6, x+ y z 2 and x, yz 0.
Write down the steps for solving a linear programming problem graphically.
33. Solve the following Game by Principle of Dominance method.
Player B
Player A |
|
34. Calculate control limits for d-chart given p = 0-05 and sample number = 5.
2 x 10 = 20
SECTION - D
IV. Answer any two of the following questions
35. Construct Fisher *s Poi from the following data and test if it satisfies Time Reversal Test.
Items |
Prices |
Expenditures | ||
2008 |
2010 |
2008 |
2010 | |
A |
12 |
10 |
96 |
90 |
B |
18 |
20 |
72 |
100 |
C |
15 |
20 |
90 |
160 |
D |
20 |
22 |
100 |
88 |
E |
10 |
08 |
90 |
64 |
36. a) From the following data, show that Town B is healthier : 5 | ||||||||||||||||||||||||||
| ||||||||||||||||||||||||||
b) Fit a parabolic trend of the form Y = a + bX + cX2 for the following |
time series : 5 | ||||||||||||
|
37. Daily wages of 60 workers are normally distributed with mean Rs. 500 and standard deviation Rs. 40. Find the number of workers getting wages
i) more than Rs. 530
ii) more than Rs. 490
iii) between Rs. 380 and Rs. 460.
38. Fit a Poisson Distribution to the following data and test for goodness of fit at 5% level of significance : | ||||||||||||
|
V. Answer any two of the following questions : 2x5=10
39. Given: p0 =376, 2g0 p0 =350
lql py= 384, lq0 px= 362.
Find :
i) Qol ( Dorbisch-Bowley )
ii) Q0, ( Marshall-Edgeworth ) and compare.
40. A machine produced 5 defective articles among 80. After some repair, the machine produced 3 defective articles among 60. Test whether the proportion of defective articles have reduced after repair, at 5% level of significance.
41. From the following 2x2 contingency table, test whether Result in a competitive examination and Employment are independent :
Employment | |||||||||
|
42. The cost of a machine is Rs. 6,000. The following gives data collected in running the machine : | ||||||||||||||||||
| ||||||||||||||||||
Determine when it is profitable to replace the machine. |
Attachment: |
Earning: Approval pending. |