Business Statistic

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UNIVERSITI TEKNOLOGI P E T RO NA S @t C OU R S E DATE TIME . GA B 2O13 B2133BUSINESS / SM STATISTTCS / QUANTITATIVE METHOD 27 MAY2008(TUESDAY) 2 . 3 0PM- 5. 30PM ( 3 hour s) INSTRUCTIONS CANDIDATES TO 1. 2. 3. 4. 5. Answer FIVE(5)outof SIX(6)questions theQuestion from Booklet. BeginEACHanswer a newpagein theAnswer on Booklet. lndicate clearly answers arecancelled,any. that if Whereapplicable, showclearly stepstakenin arriving the solutions at and indicate ALL assumptions. Do notopenthisQuestion Booklet until instructed. Note : ii. Thereare TWELVE(12)pagesin this Question Booklet including thecoverpage. Formula booklet be provided. will Univ er s j- t l Teknologi PETRONAS UNIVERSITI TEKNOLOGI P E T RO NA S @t C OU R S E DATE TIME GA B 2O13 82133. / SM BUSINESS STATISTICS / QUANTITATIVE METHOD 27 MAY2008(TUESDAY) 2 . 3 0PM- 5. 30PM ( 3 hour s) INSTRUCTIONS CANDIDATES TO 1. 2. 3. 4. Answer FIVE(5)outof SIX(6)questions theQuestion from Booklet. BeginEACHanswer a newpagein theAnswer on Booklet. lndicate clearly answers arecancelled,any. that if Whereapplicable, showclearly stepstakenin arriving the solutions at and indicate ALL assumptions. Do notopenthisQuestion Booklet until instructed. 5. Note : ii. Thereare TWELVE(12)pagesin this Question Booklet including thecoverpage. Formula booklet be provided. will Univ er s it l Teknologi PETRONAS a GAB2013/ B2133 SM Answerany FIVE(5) questions. ,r,"/ I , ,/l / U_/ TABLE Ql reportsa frequency distribution mobilephone bills for a of sample 50 students Perakduringthe monthof April2008. of in T A BLEQl: M obile Phone Bills Amount(RM) 8 0 u p to 1 0 0 Frequency | | 3 100upto 120 1 2 0u p to 1 40 1 4 0 u p to 1 60 1 6 0u p to 1 80 1 8 0u p to 2 00 I | | | | 8 12 16 7 4 questions. Basedon the abovedata,answer following the i. phone th C a l cu l a te e me a nof the m obile bills. 3 marks] ii. the Calculate standard deviation. [3 marks] iii. Use the Empirical Ruleto estimate proportion billswithintwo the of standard deviations the mean. Whatare theselimits? of i o ' iV *i 'tzd tr, - t3 marksl 2 ' , GAB2013/ B2133 SM t - (i iv. According Chebyshev to Theorem leastwhat percent the bills at of w i l ll i e b e tw e e n M 101 and 180. 56? R . 84 [3 marks] v. Calculate rangeof the sample? the [2 marks] vi. youranswer. Whatis the mode? Interpret [2 marks] v i i. yo C o mp a re u r ca l culated ean and m ode. W hat conclusion m can you makewith regards the skewness? to [2 marksj viii. Whatis the probability a student's will exceedRM 160? that bill [2 marks] L GAB2013/SM B2133 2. a. purchased typesof mutual An investor two fund namelylttikal Fund and lslamicDividend Fund. The objective was to achievesteady growth capital overthe medium longterm periodby investing a to in portfolio investments of that complywith ShariahPrinciples. The probabilitythat the funds will appreciate are 0. 7 and 0. 6 respectively. What is the probability bothfundswill appreciate that during the period? [2 marks] ii. What is the probability that lttikalFund will appreciate but l sl a mi c i vi dend D Fundwillnot appr eciate ing per iod? ur the [3 marks] ilt . What is the probability that at least one of the funds will appreciate? [3 marks] b. UniPrestige classifies graduates FirstClass,SecondClass her as Upperand SecondClassLowerin the proportions 30 percent, of 50 percentand 20 percentrespectively. UniPrestige very proudof is their graduates' employability. The probabilitya First Class g ra d u a te s u n e mployed m onthsafter gr aduation 0. 01, the i 3 is probability SecondClassUppergraduate unemployed months is 3 after graduation 0. 03 and the probability is SecondClass Lower g ra d u a te s u n e mployed m onthsafter gr aduation 0. 0. M r i 3 is Azman,a fresh graduate from UniPrestige unemployed is after 3 mo n th s f g ra d u a tion. o i. Wh a t i s th e pr obability that M r Azm an is a Fir st Class student? [4 marks] GAB 2013/SM B2133 ii. What is the probability that Mr Azman is a SecondClass U p p e r d ent? stu [4 marks] iii. What is the probability that Mr Azman is a SecondClass Lowerstudent? [4 marks] A GAB2013/SM B2133 Research has shownthat mostcar drivers are unableto ell the difference products PETRONAS Lubricant and the exclusive between brandsin the Nevertheless research has also suggested upperend marketsegments. dentify sampleone of these that 90%-of the car driverscan correctly a products. studyis conducted investigate matterand a sampleof to this A were selected. drivers 1! 9_car a. would be appropriate the above What probability distribution for youranswer. situation? Justify [2 marks] b. r G, wouldyou expect correctly How manyof the 15 drivers to identify PETRONAS brands othenlrise? or [2 marks] 10 Whatis the probability exactly of the drivers surveyed will the brand.? correctly identify PETRONAS [3 marks] c. d. Whatis the probability least10 of the drivers at surveyed will correctly identify PETRONAS the brands? 5 marks] you havedecided use Poisson probaL,ility to Suppose distribution to findthe probability the aboveproblem. for What is the probability at least 1 of the drivers surveyed will correctly identify the PETRONAS? [4 marks] wouldthe difference shouldyou decideto use How significant be Normal approximation part(e). in ( . hf, r h . - - [4 marks] 6fl =-f't e. l. ----==----.. _--/ i o ) GAB2013/SM B2133 4. According a recentsurvey, to Malaysians a meanof 7-hours sleep get of per night. A randomsampleof 50 students a publicuniversity at revealed the mean hours of sleep last night was 6 hours and 4g minutes(6. g hours). The standard deviation the sample of was 0. 9 hours. a. Statethe nulland alternate hypotheses. [2 marks] yourchoice the particular b. Justify for distribution used. [2 marks] c. Statethe decision rule,assuming s% significance a levelis used. [3 marks] d. Calculate valuefor the teststatistic. the [4 marks] e. ls it reasonable conclude to that students the particular at university sleeplessthanthe average Malaysian? [3 marks] f. ListFOUR(4) majorcharacteristics the t-distribution. of [6 marks] c GAB2013/SM B2133 5. a. A concern that usuallyariseswhen designing statistical a studyis to determining number itemsin the sample. sampleis too the of lf large,moneyis wastedcollecting data. Similarly the sampleis the if too small,the resulting conclusions be uncertain. THREE will List (3) factors determine sample the to size. [3 marks] h proportion to be within of Giventhat the estimate the population is plusor minus0. 10,with a 99 percent levelof confidence. best The proportion 0. 45. Determine sample estimate the population is of the sizerequired. [3 marks] farmwantsto estimate meannumber The ownerof a chicken the of A eggs laid per chicken. sampleof 20 chickens showsthey laid an average 20 eggs per monthwith a standard of deviation 2 eggs of per month i. . O^ v = LO S= A 2- meanif any? lf thereis none Whatis the valueof the population for whatis the bestestimate thisvalue? [3 marks] ii. interval, Fora 95 percent confidence whatis the valueof ? [3 marks] ilt . Developthe 95 percentconfidence interval the population for me a n . [4 marks] iv. to Wouldit be reasonable conclude that the population mean is youranswer. 21 eggs? Justify [4 marks] t pt GAB2013/SM B2133 'L i. o. a. at The Fridgehas six salesrepresentatives its lpoh outlet. Listed sold by each sales below is the number of refrigerators last representative month. Salesrepresentative TranAn Thu H o n gC h a o Anat Ratanapol T o n g ch a i idee Ja AntonHaig JackyTroy Num ber sold 52 (, 52 54 4B 50 50 L of How manysamples sizetwo are possible? [2 marks] ii. of the mean Selectall possible samples size two and compute n u mb e r l d . so [4 marks] ilt . the meansintoa frequency Organize sample distribution. [2 marks] lv. the mean of the population Calculate and the mean of the sa mp l e a n s. me [4 marks] Whatis the shapeof the population distribution? [2 marks] vt. Whatis the shapeof the distribution the samplemean? of [2 marks] q GAB2013/SM B2133 o. omputer, of The manufacturer eMachines,an economically-priced top the designfor a new laptop model. eMachines recently completed Two in the new laptop. wouldlike some assistance pricing management and asked to preparea pricing firms were contacted marketresearch tested the new eMachineslaptop with 150 Wee-Get-lt-Done strategy. a that they planto purchase who indicated consumers selected randomly laptop within the next year. The second marketingresearchfirm laptopwith 100 currentlaptop testedthe new eMachines Research'r'us, will be test results research companies' Whichof the marketing owners. hv. Discuss moreuseful? [4 marks] - ENDOF PAPER 10 KEY FORMULAS Lind. Marchal. and Wathen StatisticalTechniques Business in and Economics, l3th edition CHAPTER 3 . Population mean . Softwarecoefficient skewness of ck= n p: . Sample mean, raw data ' ,_ . Weighted mean r . Geometric mean N I3-11 CHAPTER 5 (n-1)(n-2)Lz s | /Y- Y31 l Sl ':- - - - :l | | /l l4-31 . Special rule of addition n 13-21 . Complement rule P(A or B) : P(A) + P(B) I5-21 I5-31 IHl wr Xr + w2 X2 + . - - + wn xn w1 + w2 + ... + wn P (A =1-P (-A ) tHI . General rule of addition P(A or B) = P(A) + P(B) - P(A and B) GM= V6JXJW-6) Geometric mean rate of increase n^" - ,f V"lu"at end of period V Value at start of period . Range Range : Largestvalue - Smallest value . Mean deviation t3-41 . S peci alrul e of mul ti pl i cati on P(A and B) = P(A)P(B) l5-5I [3-5] . Generalrul e of mul ti pl i cati on P(A and B) = P(A)P(B A) . B ayes'Theorem IH1 tH1 P (A l l B ) : . Multiplication{ormula P ( A . I. P ( B l A i P(A) . P(BIA) + P(A) . P(B A2) Is-71 *;lx - xl MD n . Population variance o , :2 ( X . Population standard deviation v) 2 - t3-7) Total arrangemenls = (m)(n) . Number of permutations IH] IHl e: n'' . Number of combinations D! @-l l 5-eI t3-el . S a m p l e v a r ia n ce [3-10] '"'- nl t1(n-r)t [5-1 0] CHAPTER 6 . Mean of a probabilitydistribution r, = ;[xP[v)] . Variance of a probabilitydistribution n-1 "z= ) fi- X) z . Sample standard deviation 16-1I [3-11] Sample mean, grouped data ,, 2fM o":;l (x-p)'P E )l . Binomial probability distribution P(x) = ,C,d(1 - n)n-x l6-21 tHI ":; Sample standard deviation,grouped data [3-12] . Mean of a binomial distribution p: nr tHl -r) o Varianceof a binomial distribution [3-13] o2:nn(l I6-51 CHAPTER 4 o Location of a percentile p Le-(n+1) . Pearson'scoefficientof skewness , 3 ( X - M e d ia n ) q Hypergeometricprobabilitydistribution ePa;: GCJ(lv sc'-') uCn tffi1 i0 0 L4-11 . Poisson probability distribution '' PF) : r;{a-ts IG. 7] 14-21 l1 CHAPTER 7 . Meanof a uniform distribution a+D a . Testinga mean, o unknown [7-1 ] . S t a n d a r dd e via tio no f a u n iform distribution ' _X p s/th . Test of hypothesis,one proportion z --l-=;-...... = in( | - T/ 1i- 11o-21 E4 . Uniform probability distribution 12 17-21 . Type ll error tlHl PE)= '' iI a < x < b b-a -l. Normal probability distribution t7-3I CHAPTEB 11 - Irt , =X, o/rfn . Varianceof the distributionof difference in means t1o_a1 nd 0 elsewhere prvr _L" i++l = gvzT . Standard normal value a:- o? -4 r" 1 n1 n2 174l . Two-sampletest of means, known o X t-X z [1 1-1] 111-21 /-u [7-5] . Two-sampletest of proportions z= i - CHAPTER 8 . Standard errorof mean ip,f n1 p") p,(1 - p,) f - [1 1-3] n2 " ' -v G . z-value, p and o known 0 tB-11 . Pooled proporlion 1 -A t n:_ n1 + n2 [11-4j .=x-Y o/:,6 CHAPTER 9 . Confidence intervalfor p, with o known x* z a, 18-21 . Pooled variance ^) " (n, - 1)s! + (n, - 1)s! nt+nz,2 1 11 -51 l$-11 . Two-sampletest of means, unknown but equal o . Confidence intervalfor p, o unknown n t' fi r Sam nlp nr^n^ri;nn 11-€] te-21 . Two-sampletests of means, unknown and unequal o" v- X n ,:++ . / a +: r flt n2 [1 1-7] l$-31 . Confidence intervalfor proportion ,- --. ^ . Degreesof freedom for unequal variance test u/-- Ftt-a n ,,_l ts1/ni + gl /n" 112 (si/nl' nt-1 , (si/n2)' nz-1 tH1 . Pairedt test [11-8] . Sample size for estimating mean ( zo Y ,= F / . Sample size for proportion / 2 Ie-5] CHAPTER 12 . Testfor comparing variances two IH] ^2 [11-ej n - p(j C H A P TER O 1 . Testing a mean, o known p)('= r/ ' -s! . Sum of squares,total Ltz-tJ ,= X -. ^ o/"vG [1o-1 ] SStntal :s/Y-Y2 .'G/ I t. -z) 1" )
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