AssignmentMFC1stSemester QAMcycle6.doc

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F-2,Block, Amity Campus

Sec-125, Nodia (UP)

Idia 2!1"!"

ASSI#N$%N&SP'#'A$

S%$%S&%'-I

Su*+ect Name

Study CUN&'

Pemaet %ollmet Num*e (P%N)

'oll Num*e

Studet Name

INS&'UC&INS

a) Studets ae e.uied to su*mit all t/ee assi0met sets

ASSI#N$%N& %&AI3S $A'4S

Assi0met A Fie Su*+ectie 6uestios 1!

Assi0met B &/ee Su*+ectie 6uestios 7 Case Study 1!

Assi0met C 85 *+ectie 6uestios 1!

*) &otal 9ei0/ta0e 0ie to t/ese assi0mets is "!: ' "! $aks

c) All assi0mets ae to *e completed as typed i 9od;pd<

d) All .uestios ae e.uied to *e attempted

e) All t/e t/ee assi0mets ae to *e completed *y due dates (speci<ied

<om time to time) ad eed to *e su*mitted <o ealuatio *y Amity

Uiesity

<) &/e ealuated assi0met maks 9ill *e made aaila*le 9it/i si=

9eeks &/eea<te, t/ese 9ill *e destoyed at t/e ed o< eac/ semeste

0) &/e studets /ae to attac/ed a sca si0atue i t/e <om

Si0atue >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

ate >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

( ) &ick mak i <ot o< t/e assi0mets su*mitted

Assi0met ?A@ Assi0met ?B@ Assi0met ?C@



6UAN&I&A&I% APP3ICA&INS IN $ANA#%$%N&

Assi0met A1. From the following data calculate the missing the missing frequency.

No. of

tablets

4-8 8-12 12-16 16-20 20-24 24-28 28-2 2-6 6-40

No. of !ersonscured

11 1 16 14 " # 1$ 6 4

%he a&erage number of tablets to cur&e fe&er was 1#.#.

2. 'ou are su!!lied the following data about heights of students in a college.

(oys )irls

Number $2 8

*&erage height +inches, 68 61

ariance of distribution # 4

Find out+a,. /n which se boys or girls is there greater &ariability in indi&idual heights.+b,. ommon a&erage heights in boys and girls.+c,. 3tandard de&iation of height of boys and girls taen together.+d,. ombined &ariability.

. %he sales of a com!any in thousands of 5s for the year 1#6 through 1#$1 aregi&en below

'ear 1#6 1#66 1#6$ 1#68 1#6# 1#$0 1#$1

3ales 2 4$ 6 #2 12 1#0 2$

7stimate the sales figure for the year 1#$2 using an equation of the form. 'ab

where year and ' sales.

4. Find the coefficient of correlation between 9 and '.

9 1 2 4 6 $ 8 #

' 12 11 1 1 14 1$ 16 1# 18



. %he following are the inde of annual !roduction of a certain commodity assume yearly cycles and find out the trend &alues.

'ear 1#41 1#42 1#4 1#44 1#4 1#46 1#4$ 1#48 1#4#

/nde 22 210 201 21 22 24 2 22 2

'ear 1#0 1#1/nde 24# 26



Assi0met-B

1. * die is tossed 120 times with the following results

No. turnedu!

1 2 4 6 %otal

Frequency 0 2 18 10 22 1 120

%est the hy!othesis that the die is unbiased.

2. (allast must weigh 10 g. /t can be made from two raw materials * +with acost of 5s. 20 !er unit, and ( +with a cost of 5s. 80 !er unit,. *t least 14 unitsof ( and no more than 20 units of * must be used. 7ach unit of * weighs gand each unit of ( weighs 10 g. :ow many units of each ty!e of rawmaterial must be used for a !roduct to minimi;e cost"

. * com!any is trying to decide whether to bid for a certain contract or not.%hey estimate that merely !re!aring the bid will cost 5s.10000. /f their com!any bid then they estimate that there is a 0< chance that their bid will be !ut on the =short-list= otherwise their bid will be re>ected. ?nce =short-listed= the com!any will ha&e to su!!ly further detailed information +entailingcosts estimated at 5s.000,. *fter this stage their bid will either be acce!tedor re>ected. %he com!any estimates that the labor and material costsassociated with the contract are 5s.12$000. %hey are considering three !ossible bid !rices namely @1000 @1$0000 and @1#0000. %hey estimatethat the !robability of these bids being acce!ted +once they ha&e been short-listed, is 0.#0 0.$ and 0. res!ecti&ely. Ahat should the com!any do and

what is the e!ected monetary &alue of your suggested course of action"

Case Study

%he Be!artment of 7n&ironment has theori;ed that !ollution le&els are higher in winter +/C / Duarter, than summer +// C /// Duarter, and that they are increasing o&er the years.%he following data was collected6uate I II III I

1##6 2# 246 21 282

1##$ 01 22 22$ 2#11##8 04 2# 2# 2#61### 06 26 240 00a. Betermine the seasonal indices and deseasonali;e the data. b. alculate the regression line that is described by this data.c. *re both the assum!tions of the de!artment of 7n&ironment correct" 'ou may test to asignificance le&el of 0.0.



Assi0met "

1. /f * and ( are inde!endent e&ents with E +*, 0.2 E +(, 0.4 and E +* (, 0.then E +*G(, C E +(G*, area. 0.2 C 0.4 b. 0.600 C 0.2$

c. 0.$2 C 0.2$d. 0.60 C 0.60e. 0.42 C 0.

2. /f you want to test the whether the change is significant on the mean body weight on agrou! of randomly chosen !eo!le after a !articular diet is administered you shouldem!loya. Eaired-t test b. * sim!le t testc. *n inde!endent single sam!le t testd. *n inde!endent two sam!le t test

e. ariance test. luster sam!ling isa. a non-!robability sam!ling method b. the same as con&enience sam!lingc. a !robability sam!ling methodd. Hudgement sam!linge. None of these alternati&es is correct.

4. * IE !roblem has decision &ariables and constraints. :ow many non basic&ariables are there"a. b. c. 8d. $e. 2

. /f a random &ariable 9 is distributed normally with mean 0 and &ariance 2 find outE+9J40,a. 0.222 0 b. 0.0228c. 0.0#4d. 0.02e. 0.0#1#

6. * sam!ling method in which the !o!ulation is di&ided into grou!s such that each grou!has a small &ariation with in itself and a wide &ariation between themsel&es and sam!lesare drawn from each grou! is nown asa. 5andom sam!ling b. 3tratified sam!lingc. luster sam!ling



d. 3ystematic sam!linge. Hudgmental sam!ling

$. %he following linear trend e!ression was estimated using a time series with 1$ time !eriods.%t 12#.2 K .8t%he trend !ro>ection for time !eriod 18 isa. 68.4 b. 1#.8c. 1#$.6d. 6.84e.1#.8

8. /f the sam!ling fraction nGN is less than 0.0 the standard error of the sam!le mean isgi&en bya. LG Mn b. LGMn M+N-n,G+N-1,Oc. LGMn M+ nGN,d. LGMn M+N-1,G+N-n,e. L

#. %he sam!le mean is the !oint estimator of a. P b. Lc. xd. pe. 3

10. * regression analysis between sales +' in Q1000, and ad&ertising +9 in dollars,

resulted in the following equation'Q 0000 K 4 9%he abo&e equation im!lies that ana. /ncrease of Q4 in ad&ertising is associated with an increase of Q4000 in sales b. /ncrease of Q1 in ad&ertising is associated with an increase of Q4 in salesc. /ncrease of Q1 in ad&ertising is associated with an increase of Q4000 in salesd. /ncrease of Q1 in ad&ertising is associated with an increase of Q4000 in salese. /ncrease of Q4 in ad&ertising is associated with an increase of Q0000 in sales

11. * random ariable has the following !robability distribution P()

0 0.01 0.12 0.1 0.204 0.2 0.106 0.1Ahat is the &alue of E+1R 9R,"



a. 0.80 b. 0.2c. 0.1d. 0.10e. 0.0

12. %wo cards are drawn without re!lacement from a dec of 2 cards. Ahat is the !robability of drawing two queens"a. 1G221 b. 1G121c. 1G21d. 1G421e. 1G111

1. *ssume a binomial !robability distribution with n 40 and ! .. om!ute themean and standard de&iation of the random &ariable.a. Sean 22 and 3B .146 b. Sean 20 and 3B .146c. Sean 24 and 3B .146d. Sean 26 and 3B .146e. Sean 18 and 3B .146

14. From a calendar for 200 we sam!le e&ery 11th day starting from Hanuary $thT whatty!e of sam!ling is this"a. Hudgemental sam!ling b. 3im!le random sam!ling without re!lacementc. 3ystematic sam!lingd. luster sam!linge. 3im!le random sam!ling with re!lacement

1. /n a goodness-of-fit test where the sam!le si;e is 200 there are categories and thesignificance le&el is .0. %he critical &alue of U2 isa. #.488 b. 11.0$0c. 4.$$d. 4.88$e. 2.66#16. %o conduct the sign test we assumea. %he !o!ulation is normally distributed b. %he scale of measurement is inter&al

c. %he sam!les are de!endentd. %here are at least 20 obser&ations in the sam!lee. %here are minimum 2 obser&ations in the sam!le

1$. * time series com!onent which cannot be analysed by a mathematical model isa. %rend b. 3easonalc. yclical



d. 5andome. yclical and random

18. Ahich of the following cannot be inferred from a scatter diagram"a. ause effect relationshi!s b. Eresence or absence of relationshi!sc. Iinear or cur&ilinear relationshi!d. Birect or in&erse relationshi!e. *ll can be studied

1#. Ahich of the following is true of the coefficient of determination"a. /t is the square of the correlation coefficient b. /t con&eys the etent to which the &ariations are e!lained by the regression equationc. /t con&eys the etent to which the &ariations are une!lained by the regressionequationd. (oth +a, and +b, abo&ee. (oth +a, and +c, abo&e

20. Ahen formulating %rans!ortation IE !roblems constraints usually deal witha. %he number of items to be trans!orted b. %he shi!!ing costs associated with trans!orting goodsc. %he distance goods are to be trans!ortedd. %he number of origins and destinationse. %he ca!acities of origins and requirements of destinations

21. /f the coefficient of correlation between two &ariables and is equal to one thenthere isa. No relationshi! between &ariables 9 and ' b. * !erfect !ositi&e linear relationshi! between &ariables 9 and '

c. * !erfect negati&e linear relationshi! between &ariables 9 and 'd. * cause and affect relation eists between 9 and 'e. * wea association between &ariables 9 and '

22. *n in&entor claims that her new !etrol additi&e will drastically enhance the mileageof the !etrol !owered cars. urrently the &ehicle runs as a&erage mileage 1 m for onelitre of !etrol. %he a!!ro!riate null and alternati&e hy!otheses in e&aluating her claimwill be +in the order of :0 and :a,a. 91 9 J 1 b. 9 1 9 R 1c. 9 J 1 9 1

d. 9 1 9 1e. 9 1 9 R 1

2. *fter deseasonalisation a time series can be re!resented asa. ' 3 / b. ' % 3 /c. ' % /d. ' % 3 /



e. ' % 9 3 9

24. /f one regression coefficient is greater than unity then the other must bea. )reater than the first one b. 7qual to unityc. Iess than unityd. 7qual to ;eroe. Iess than the first one

2. Ahich of the following statements is false"a. /n a !ro!er random sam!ling e&ery element of the !o!ulation has a nown +and oftenequal, chance of being selected b. %he !recision of a sam!le mean or sam!le !ro!ortion de!ends only u!on the sam!lesi;e +and not the !o!ulation si;e, in a !ro!er random sam!lec. on&enience sam!ling often leads to biases in estimates since the sam!le is often notre!resentati&e of the !o!ulationd. /f a sam!le of 1000000 families is randomly selected from all of Vota +with about8000000 families, and the a&erage family income is com!uted then the true &alue of thefamily income for all families in Vota is nowne. None of the abo&e

26. For two &ariables and y to be inde!endent of each other which of the followingmust be truea. L Ly

b. L 2 L 2

y

c. o& + y, 0d. y x =

e. 7+, 7+y,

2$.Ahich of the following is a true measure of regret"a. Saimum !ossible !rofits W reali;ed !rofits b. Saimum of minimum !rofits W minimum of minimum !rofitsc. Saimum !ossible !rofits W foregone !rofitsd. Saimum of maimum !rofits W maimum of minimum !rofitse. Saimum !ossible !rofits W minimum of maimum !rofits.

28. * sam!le of 1 is drawn from a !o!ulation si;e of 100. %he finite !o!ulationcorrection factor isa. 0.10 b. 0.184c. 0.2d. 0.84e. 0.#266



2#. Ahich of the following re!resents re!etiti&e and !redictable mo&ements around thetrend line within a time !eriod of one year or less"a. 3ecular trend b. yclical fluctuationc. 3easonal &ariation

d. /rregular &ariatione. %em!orary &ariation.

0. Ahich of the following is true with res!ect to the method of least squares"a. 3um of the squared &alues of the hori;ontal distances from the regression line to

the y-ais and the corres!onding !oints of the de!endent &ariable is minimi;ed b. 3um of the squared &alues of the &ertical distances from the regression line to

the -ais and the corres!onding !oints of the inde!endent &ariable isminimi;ed

c. 3um of the squared &alues of the hori;ontal distance from each !lotted !oint based on the obser&ations to the regression line is minimi;edd. 3um of the squared &alues of the &ertical distance from each !lotted !oint to the

regression line is minimi;ede. None of the abo&e.

1. %he !robability that an obser&ation following a normal distribution will lie within PX 1.L isa. #. < b. 1#.0<

c. 40.<d. 0.0<e. 80.6<

2. *rri&als of customers at an *%Ss follow the Eoisson distribution. %he a&eragearri&als !er hour is 6. %he !robability of eact 6 arri&als in an hour isa. 1.00 b. 0.0c. 0.2

d. 0.16e. 0.10. /f a random sam!le of si;e 1 is selected from a symmetrical !o!ulation with a

unique mode the degrees of freedom of the obser&ation isa. 14 b. 1c. 16



d. 1$e. 18

4. /n regression analysis YYYYYYYYYYY re!resents how much each unit change of theinde!endent &ariable changes the de!endent &ariable.

a. 3lo!eb. ' W interce!tc. 3tandard error of estimated. Be!endent &ariablee. oefficient of correlation

. /f two &ariables 9 and ' are !erfectly !ositi&ely correlated and their standardde&iations are and 10 res!ecti&ely then the co&ariance isa. 0.40b. 0.0c. 2.00d. 4.00e. 0.00

6. %he sam!le !ro!ortion of ri!e mangoes in a large consignment is 0.$. /f the u!!er limit of a confidence inter&al for the !ro!ortion of ri!e mangoes in the lot is 0.86 thelower limit is

.a 0.64

.b 0.4

.c Be!ends on the confidence le&el

.d Be!ends on the sam!le si;e

.e (oth +c, and +d, abo&e

$. * contingency table for two attributes consists of 24 cells. %he number of degrees of freedom for the chi square test statistic is

a. Be!ends on the number of rows and columns

b. 24c. 2d.

14e. 1

8. Ahich of the following statements are true" b. Ahen the !ercent of trend is below 100 the relati&e cyclical trend is negati&e

and con&ersely



c. Ahen the !ercent of trend is below 100 the relati&e cyclical trend is !ositi&eand con&ersely

d. Ahen the !ercent of trend is below 100 the relati&e cyclical trend is negati&e but not con&ersely

e. Ahen the !ercent of trend is below 100 the relati&e cyclical trend is !ositi&e but not con&ersely

f. %he two measures ha&e to be considered inde!endently

#. Ahich of the following is not true of random &ariations"a. %hey can be identified

b. /t cannot be e!lained mathematicallyc. %hey occur in a random manner d. %hey cannot be easily !redictede. *ll are true

40. %he loss from stocing a unit of a !roduct not sold is 5s.0 while the !rofit fromselling a unit of that !roduct is 5s.0. %he minimum !robability of selling an etra unitthat will >ustify stocing it isa. G

b. 2Gc. G8d. 2G8e. G4

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AssignmentMFC1stSemester QAMcycle6.doc