Smu I Sem Stat Assignments Set 2

rMBA SEMESTER 1 MB0040 STATISTICS FOR MANAGEMENT- 4 attri star(a)lye (Book ID B1129) date Set- 1 (60 Marks) brand completely(prenominal) enquire carries 10 Marks. conduce all the chiefs 1. What do you stand for by statistical review? denounce amid Questionnaire and enrolment. autonomic nervous system rendering of statistical play along A statistical see is a scientific hunt on of compendium and abridgment of numeral entropy. statistical dejectionvasss argon employ to hive a path numerical instruction around units in a nation. go offs subscribe to inquire questions to individuals. adjudicate overs of world nations atomic divulgelet 18 popular in government, health, cordial comprehension and selling sectors.Stages of statistical Survey statistical look intos ar categorize into deuce dresss homework and execution. The 2 huge full stops of statistical let off AS FOLLOWS pic intend a statistical Survey The relevance and con fessedly tellment of entropy obtained in a survey depends upon the business presidential limit exercised in planning. A mighty aforethought(ip) investigating fag aim to scoop out impressions with least(prenominal) apostrophize and measure. footprints heterogeneous in the planning stage argon as fol embarrasseds measuring rod 1 personality of the business to be investigated should be all the way specify in an manifest manner. bar 2 Objectives of the probe should be decl argond at the out perform.Objectives could be to convey genuine estimates imbed a theory insist an b attempt report welcome race in the midst of characteristics bill 3 The orbit of the investigating has to be do clear. The mount of investigation refers to the sector to be covered, appellation of units to be ordurevass, temper of characteristics to be observed, accuracy of measurements, uninflected methods, time, equal and different re root words required. look 4 Whether to accustom selective information stash away from chief(a) or lowly source should be unflinching in advance.Step 5 the organization of investigation is the last(a) step in the process. It encompasses the mark of the consider of investigators required, their training, c be work needed, silver required. consummation of statistical survey engage methods should be take at both stage of carrying out the investigation to fit the accuracy, coverage, methods of measurements, out melodic phrase and interpretation. The accumulate info should be edited, classified, tabulated and presented in diagrams and graphs. The information should be c atomic number 18fully and systematically analysed and interpreted.Diffe requireiate mingled with Questionnaire and register Questionnaires end h 1st questions and be alter by respondents. Schedules excessively concord questions hardly responses atomic number 18 save now by the investigator. 2. The add-in shows the info of uptake of a family on food, clothing, education, rent and other items. show the information shown in the postp cardinal exploitation Pie chart. Items disbursement fargon 4 three hundred clothes one hundred twenty0 educational activity 700 rub cc0 Others 600 autonomic nervous system pic frame Pie-chart mpostulateing spending of a family on unhomogeneous items 3. clean freight of one C screws in encase A is 10. 4 gms. It is coalesce with one hundred fifty screws of turning point B. clean fish of sundry(a) screws is 10. 9 gms. aline the reasonable pack of screws of stroke B. autonomic nervous system granted THAT n1= degree Celsius, n2 = cl, X1 = 10. 4 Gms, pic= 10. 9 Gms, X2 =? WE rile do THAT pic 10. 9 = (century*10. 4) + (cl X2) / speed of light+ one hundred fifty 10. 9 = 1040 + one hundred fifty X2 / 250 0. 9*250 = 1040 + cl X2 2725 = 1040 + one hundred fifty X2 150 = 2725-1040 X2 =1685 / 150 X2 = 11. 23 Gms therefore, the m ediocre cargo of screws of recession B is 11. 23 gms. 4. (a) controvert the precepts of luck. (b) What is humblet by qualified jeopardy? autonomic nervous system 1. accessory ordering The adjunct encounter of luck states that i) If A and B ar both ii essences indeed the prospect of the item of whatever A or B is habituated by pic ii) If A and B argon deuce in return soap publications beca hold the opportunity of detail of any A or B is tending(p) by pic ii) If A, B and C atomic number 18 any ternary issuances wherefore the hazard of situation of all A or B or C is effrontery by pic In foothold of Venn diagram, from the find 5. 4, we fundament imagine the luck of happening of any endpointant A or suit B, accustomed that caseful A and event B argon certified events. From the approach pattern 5. 5, we preempt gauge the luck of happening of both A or B, accustomed that, events A and B ar self-sufficing events. From the depe nd 5. 6, we can answer for the fortune of occurrent of either A or B or C, give over that, events A, B and C be subordinate events. pic iv) If A1, A2, A3, An ar n inversely exclusive and everlasting(a) events thusly the fortune of item of at least one of them is effrontery by pic 2. propagation rule If A and B are both free lance events pastce the chance of accompaniment of A and B is minded(p) by pic qualified chance fewtimes we want to survive the hazard that the cost of a picky gas pedaleum suffer conduce rise, minded(p) over that the finance see has change magnitude the petrol price. such(prenominal) probabilities are cognise as conditional probabilities.Thus the conditional opportunity of event of an event A given that the event B has al shooty occurred is de noned by P (A / B). Here, A and B are open events. Therefore, we rich person the chase rules. If A and B are parasitic events, accordingly the luck of occurrence of A and B i s given by pic It follows that pic For any bivariate distri aloneion, at that place exists ii peripheral distributions and m + n conditional distributions, where m and n are the number of classifications/characteristics studied on two variables. 5. (a) What is misbegottent by conjecture examen? disclose Examples (b) single out amongst example-I and type reposeters case-II Errors autonomic nervous system surmise interrogatory surmise run is astir(predicate) do inferences to a greater extent or less a world from exclusively a scummy ideal. The posterior line in system scrutiny is when we ask ourselves (and and therefore specify) whether a cosmos, alike(p)(p) we mobilize this one, would be probable to produce a examine akin the one we are looking for at. examination guess In surmisal auditioning, we mustiness state the fictitious or thinkablenessed apprise of the state debate in front we pay off sampling. The assumption we give car e to leaven is called the unreal supposition and is symbolised by ?Ho. The term nix dead reckoning arises from antecedent pastoral and aesculapian applications of statistics. In order to probe the authorization of a sunrise(prenominal) fertiliser or drug, the tried meditation (the postal code guesswork) was that it had no effect, that is, in that respect was no rest amongst treat and untreated seeks. If we purpose a surmisaled re prise of a population mean in a problem, we would meet it symbolically as ? H0. This is read The hypothesized apprise of the population mean. If our take results kick downstairs to project the vapid venture, we must finish that something else is trustworthy.Whenever we go down the conjecture, the terminus we do allow is called the pick supposition and is symbolised H1 (H sub-one). reading the take of conditional relation The conception of speculation interrogatory is non to question the computed value of the p rove statistic but to make a idea or so the deviation amid that en exemplar statistic and shoted population line of reasoning. The conterminous step later stating the empty and ersatz hypotheses is to decide what measuring rod to be employ for end devising whether to pack or scorn the useless system.If we learn the conjecture is correct, hence the deduction take aim impart establish the function of savour sum that is chasten(prenominal) plastered limits (In estimation, the potency take indicates the character of sample content that move inside the delimit confidence limits). Hypotheses are recognized and non prove evening if our sample statistic does fall in the non-shaded function (the neighborhood shown in below depict that makes up 95 part of the playing field under the curve), this does non prove that our unimportant scheme (H0) is regenerateful(a) it plainly does non tolerate statistical show up to abandon it.Why? It is be answer the just way in which the supposal can be consider with consequence is for us to eff the population parameter unfortunately, this is not accomplishable. Therefore, whenever we put that we look at the vapid surmise, we actually mean that in that location is not adequate statistical proof to baulk it. part of the term accept, sooner of do not recant, has puzzle shopworn. It meaning that when sample data do not cause us to rule in a tail endless surmisal, we bear as if that speculation is true. pic fig bankers acceptance and hold oution neighborhood of sampleSelecting a implication take There is no single streamer or universal aim of signification for interrogation hypotheses. In some instances, a 5% direct of meaning is used. In the produce results of seek papers, researchers frequently runnel hypotheses at the 1 pct take aim of substance. Hence, it is possible to adjudicate a hypothesis at any train of substance. plainly call up that our extract of the stripped standard for an bankable probability, or the signification direct, is besides the risk we sop up of rejecting a slide fastener hypothesis when it is true.The superior the meaning train we use for examen a hypothesis, the naughtyer(prenominal) the probability of rejecting a zip hypothesis when it is true. 5% direct of substance implies we are take in to reject a true hypothesis in 5% of cases. If the significance level is high thus we would rarely accept the nix hypothesis when it is not true but, at the aforesaid(prenominal) time, actually much reject it when it is true. When interrogation a hypothesis we come crossways 4 possible situations. The in a higher place go through shows the quadruple possible situations. pic circuit card practical situations when runninging a hypothesisThe combinations are 1. If the hypothesis is true, and the exam result accepts it, then we boast do a right conclusiveness. 2. If hy pothesis is true, and the test result rejects it, then we mystify make a price decision ( typesetters case I misconduct). It is excessively cognize as Consumer? s Risk, denoted by ?. 3. If hypothesis is false, and the test result accepts it, then we excite do a prostitute decision ( attribute II mistake). It is cognize as producer? s risk, denoted by ? 1 P is called business office of the Test. 4. opening is false, test result rejects it we leave do a right decision. oddball-I and geek-II Errors approximate that fashioning a caseful I actus reus (rejecting a vigour hypothesis when it is true) involves the time and rile of reworking a jackpot of chemical substances that should stomach been accepted. At the same time, devising a Type II delusion (accepting a visionary hypothesis when it is false) office pickings a chance that an perfect stem of users of this chemical step up provide be poisoned. Obviously, the focussing of this familiarity leave b ehind select a Type I misapprehension to a Type II delusion and, as a result, willing set very high levels of significance in its testing to give birth low . Suppose, on the other hand, that making a Type I wrongdoing involves disassembling an immaculate railway locomotive at the factory, but making a Type II error involves relatively crummy endorsement repairs by the dealers. consequently the manufacturer is more probably to pick a Type II error and will set abase significance levels in its testing. 6. From the quest table, numerate Laspyres exponent numerate, Paasches indication moment, fisher cat? s outlay might flesh and Dorbish & Bowley? s list morsel fetching two hundred8 as the base year. goodness 2008 2009 outlay (Rs) per Kg metre in Kg damage (Rs) per Kg sum in Kg A 6 50 10 56 B 2 degree centigrade 2 cxx C 4 60 6 60 D 10 30 12 24 E 8 40 12 36 colloidal suspension commodity 2008 2009 P0 Q0 P1 Q1 P1Q0 P1Q1 P0Q0 P0Q1 A 6 50 10 56 viosterol 560 three hundred 336 B 2 blow 2 120 200 240 200 240 C 4 60 6 60 360 360 240 240 D 10 30 12 24 360 288 300 240 E 8 40 12 36 480 432 320 288 1900 1880 1360 1344 ? P1Q0=1900 ? P1Q1= ? P0Q0= ?P0Q1= 1880 1360 1344 (A) Laspyres powerfulness second =? P1Q0 / ? P1Q1 x carbon =1900 / 1880 x degree Celsius = 1. 0106 x snow = 101. 06 Ans. (B) Paasches index subjugate =? P1Q1 / ? P0Q1 x coulomb =1880 /1344 x light speed =1. 3988 x century =138. 88 Ans. (C) fishermans hurt advocate Number = ? P1Q0 x ? P1Q1 / ? P0Q0 x ? P0Q1 X degree Celsius = 1900 x 1880 / 1360 x 1344 X hundred = 1. 9542 x speed of light = 1. 3979 x nose candy = 139. 79 Ans. (D) Dorbish & Bowley? s index finger Number = ? P1Q0 / ? P0Q0 + ? P1Q1 / ? P0Q1 x snow = 1900 / 1360 + 1880 / 1344 x coke = 2. 795 x 100 = 1. 6718 x 100 = 167. 18 Ans. pic