Pre University Board 2011 P.U.C. Commerce (CEBA) Statistics - Question Paper

1. e3ed &es3 .sodded ?

6 t t 6

3.    o    s30ed.o>    eodcOiD.

2>    c-5    o    _0    vJk    -/*    c<

4.    suo sterfofc d.eoS)    eslste 3 draeo&sirorfrWil toodi

6 *>     &    <4

loa.

5.    wffr )3d?fo> sJoZjisj oaS* sJofSafcsk, S73,& sodctoQ.

       <4 6 -9

6.    oci)    &3dc!oi<), P ( - 0-8 < Z < + 0-8 ) = 0-5762 >ctii Ira&srt, P(z< + 0-8) tfoe&kssccoo.

7.    dfsesi &odde?& ?

8.    H, : p. ₁ < V¹2 &343rt H₀ 5?S CJdoiiO.

9.    sid& *ort,3o aoddesk ?

10.    otosC rtors 3ako3,rac3<Q, V1) doid od> rbrad? sodcsoe.

)ri - B

II. CdJ3)CraddL0 3a    STOOj :    10 X 2 = 20

11.    ssfieSedfid e>0d-02Sris?) ^l&eodr3    sJod.w sraA &dOA>.

   S'    ol #4 _o

12.    #i ds?F\rf d;>o$rts?od &koeo wafc-d.ok dd sakcto, erodoi?A*i sSedrf dz3 .otfdcfo dodDoQcoO :

o    <4

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

e    . *    l

15.    &3drlo& <sddo    eodctoO.

16.    Soodi d,'*⁷³³ c*rfc&<), so3osSoo 9 pSo.e. ² stock &rai33/(, &&&qraF02i osS'ok? Jo&ZnBC&O.

17.    sjsio 3o3rtjs adFssrteto, sssjOA

- =t & 6

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.

^v    C"    CO    <

20.    ,edoi iidd: rttraskrri? >1.

to

25.    orts?od    riaookffci, erodoiefl&, 3d tfcrasjO

fi    0    si    1

26. #i    sue; $,er3r1 5 OTdrts*    riratforttf dojo3 dd sSdrts

oc&cocOiO :

(&Era₆$rrfe?rt sjjs)

doetod ei>o ,er3r1 4 srodrte*    ricraslOrte dojsotf sd sSdrttfev

OCsDooaCuDO.

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,

       '    l    co ⁷    eJ

rfsjss3rtss<)

i)    odi did,

ii)    ijQriod 3o2 djs>?j didrt &es3) aoedj&ao ?

28.    t-od; ssradjs d3,d oiraOTddjs sod: orsrte &$&.

29.    ⁿu,odi sdo&od 50 ds? rfs&jarfo&ci Jrtck&scraftrf. w    jJodd

28 4.rra,o aoartjs >c&3 ac5oS 5 a.ro,o d. w 2do& sfcfytf 30 d.nre,orts?fto3 e?sd:> <aodo ?xas$ ensSotfwakde aodo 1% aSr did, dOed.

30. sodo    .prrtsfe Soodo &?do3o> srtdSo*), 3sMod

eso3risfcb, riddi.

<4

X : 3. 5, 4, 2, 1

5% eJ53oF-3o> doldt,    >z3v$o0 3    >o2o d

sScSofc doea.

31. s 3<od dortod. tow, &ot.Sfoo ddt> (Dskxkrt dcid rirosJO

_    wo*    

eorts?,, cdrad)de rtdodr d₆3a₆?S dc&e <aodo doed.

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.

(<&oz$ acrorrWrt ste>)

?Sds? deOeoi)    rtdoc&K we3esO >j?id do.e;3 ;8*bss3r( 3odoiodod

SoOrteto todCuoO.

33.    & ds&od edo&F    33/d dqo&od .pa.

&3rd a

34. p = 0-05 Sourt rfdojs?3 = 5 aodo Iratis/i d-ofc Scdoors odoSooDoO.

>2e>ri - D

IV. &    oirasj)Cjsddf3 >tic&    ero3Oft :    2 x 10 = 20

35. &    P_n. sk tfockfcack,    too si&otf

-*>    *    V i    t    '    0-0

36. a)    dso2jris?orf B sdfcracfcjck a& esdert₆OTAc3d <js?Oft : 5

b) &t dtftfod %i>o jerSrl Y= a + bX+ cX² dostfd stos3>eo& sakrf' riooiraesSft :    5

37.    60 5)DF3d ?3rira<)ri ?ocwy0oo &Jd. 500 Sortra    <az3o?3 djs. 40 ssks? adffok? ?i>s5OTfcrf. >rfrt0,

i) do. 530 d₄og

11) . do. 490 a₄oaS

iii) d. 380 d 353ft do. 460 d ?Si>s5

rbsj enord 3o33.o>;& soc&coaoD.

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38.     c&osi stofs⁶' dcfo&Fi sJooioesS 3>rto 5% 053oF oar    sbOedj.

- E

& 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(,

i)    0_O1 (c3's!Fq3⁶' - zP<D) 5>,

ii)    0_O1 (s

ocSoSctoD 33-5 rt sloeC.

40.    ocb o>o4 80    5 doessis    dd&o> rfo3d, w oio4 60 3 d/aesSs steb.rts? erasa*. draesSsypO 3dJs3osj4 ddc& rfod srfioiraAdoSie <aodo 5% 053oF sbid, sSOeAt. ,

4]. cca 2x2    loesatfaori    sJOesre    asrOa

Vorfjerf Xj&o&pSe <aocb sjbe :

erozZ&eri

42, iock o&o3,d ddato dja. 6.000. o>o3,rt o?3o> adsroA StffW

d'SQ orSsb, &daAd :

-j    l

ate>> gDol c&o.sScfo, tjrfejscxodd erscoStfsrsrto d aozoodck,

u        K        _fi    I

tsct&ib&oi&e.

( English Version )

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.

SECTION - A

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.

SECTION-B

II. Answer any ten of the following questions :    10 x 2 = 20

11.    Briefly explain Registration method in vital statistics.

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.

SECTION - C

III. Answer any eight of the following questions :    8 x 5 = 40

24.    Explain steps involved in the construction of Consumer Price Index Number.

26. Obtain trend values by 5 weekly moving averages method for the following time series. Plot original and trend values on a graph.

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.

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.

{ ONLY FOR BLIND STUDENTS ]

Write down the steps for solving a linear programming problem graphically.

33. Solve the following Game by Principle of Dominance method.

Player B

34. Calculate control limits for d-chart given p = 0-05 and sample number = 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.

SECTION - E

V. Answer any two of the following questions :    2x5=10

39.    Given: p₀ =376, 2g₀ p₀ =350

lq_l p_y= 384, lq₀ p_x= 362.

Find :

i)    Q_ol ( 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 :