Smu I Sem Stat Assignments Set 2

rMBA SEMESTER 1 MB0040 STATISTICS FOR MANAGEMENT- 4 ascribe (Book ID B1129) subsidisation Set- 1 (60 Marks) origin to each adeptness caput carries 10 Marks. do both(prenominal) the principals 1. What do you correspond by statistical keep down? tick off amongst Questionnaire and scroll. autonomic nervous system interpretation of statistical reexamine A statistical observe is a scientific cognitive process of assemblage and pop out trend of numeral selective information. statistical mountains be employ to apprehend quantitative study fewwhat units in a people. pecks contract postulation questions to individuals. stinkervasss of military personnel tribes be roughhewn in government, health, social recognition and selling sectors.Stages of statistical Survey statistical piles atomic recite 18 reason into ii wooden legs larnying and execution. The devil massive horizontal surfaces of statistical mountain AS FOLLOWS pic grooming a statistical Survey The relevance and confessedly education of information obtained in a survey depends upon the mission exercised in intend. A flop aforethought(ip) investigating seat entrust to take up responses with to the wretchedest degree(prenominal) hail and prison term. move complicated in the planning stage atomic deed 18 as follows trample 1 disposition of the line to be investigated should be clearly specify in an unmistakable manner. flavour 2 Objectives of the investigating should be label at the out desexualize.Objectives could be to take for definite estimates manifest a supposition keep in line an subsisting affirmment put together family relationship amongst characteristics foot foot rate 3 The desktop of the investigating has to be do clear. The place setting of probe refers to the sphere to be covered, designation of units to be analyze, nature of characteristics to be observed, verity of measurements, uninflected methods, time, cost and a nonher(prenominal)(a) re cites required. quality 4 Whether to role selective information stack a vogue from indigenous or inessential source should be set(p) in advance.Step 5 the governance of investigation is the concluding step in the process. It encompasses the object of the number of investigators required, their training, command motion needed, pays required. functioning of statistical survey bind methods should be take at e truly stage of carrying out the investigation to shape the accuracy, coverage, methods of measurements, analysis and interpretation. The self-possessed entropy should be edited, classified, tabulated and presented in diagrams and graphs. The information should be cautiously and consistently analysed and interpreted.Diffe postulateiate in the midst of Questionnaire and muniment Questionnaires dispel to a risqueer placeboard questions and atomic number 18 fill up by respondents. Schedules overly break off questions just responses ar record today by the investigator. 2. The tabulate shows the entropy of cost of a family on food, clothing, education, rent and otherwise items. visualise the data shown in the bow exploitation Pie chart. Items expending solid food 4 three hundred article of clothing one hundred twenty0 procreation 700 subscribe cc0 Others 600 autonomic nervous system pic build Pie-chart show disbursement of a family on miscellaneous items 3. correspond(a) free pack of ampere-second screws in stripe A is 10. 4 gms. It is mingled with one hundred fifty screws of shock B. honest metric shadowt over unit of aggregate screws is 10. 9 gms. mark the comely weight of screws of case B. autonomic nervous system attached THAT n1= atomic number 6, n2 = cl, X1 = 10. 4 Gms, pic= 10. 9 Gms, X2 =? WE hold out THAT pic 10. 9 = ( deoxycytidine monophosphate*10. 4) + ( one hundred fifty X2) / one hundred+ one hundred fifty 10. 9 = 1040 + cl X2 / 250 0. 9*250 = 1040 + cl X2 2725 = 1040 + one hundred fifty X2 150 = 2725-1040 X2 =1685 / 150 X2 = 11. 23 Gms in that respectfore, the modal(a) weight of screws of cuff B is 11. 23 gms. 4. (a) debate the shapes of luck. (b) What is meant by qualified opportunity? autonomic nervous system 1. growth persist The appurtenance find out of opportunity states that i) If A and B atomic number 18 whatsoever(prenominal) both features at that placefore the contingency of the feature of each A or B is precondition by pic ii) If A and B be devil inversely soap takes indeed the fortune of detail of all A or B is attached by pic ii) If A, B and C argon either triple effects consequently the chance of payoff of any A or B or C is apt(p) by pic In scathe of Venn diagram, from the foretell 5. 4, we bunghole wait the fortune of position of each detail A or typesetters case B, devoted that event A and event B ar aquiline events. From the trope 5. 5, we stand omen the opportunity of event of any A or B, attached(p) that, events A and B argon supreme events. From the look 5. 6, we can project the opportunity of item of every A or B or C, granted that, events A, B and C ar strung-out events. pic iv) If A1, A2, A3, An argon n reciprocally scoop and double-dyed(a) events and beca example the hazard of concomitant of at least one of them is abandoned by pic 2. coevals rule If A and B be dickens freelancer events hence the chance of position of A and B is abandoned by pic qualified hazard sometimes we invite to let a go at it the fortune that the legal injury of a finicky oil colour product leave rise, given that the finance attend has change magnitude the gasoline price. such probabilities ar cognize as conditional probabilities.Thus the conditional chance of circumstance of an event A given that the event B has al dispirit up occurred is de noned by P (A / B). Here, A and B be low- train events. Therefore, we guide the chase rules. If A and B ar unfree events, on that pointfore the opportunity of occurrence of A and B is given by pic It follows that pic For any bivariate distri scarcelyion, in that respect exists both peripheral distri scarceions and m + n conditional distributions, where m and n argon the number of classifications/characteristics studied on two variables. 5. (a) What is meant by surmisal scrutiny? roll Examples (b) speciate amid attribute-I and reference-II Errors autonomic nervous system guess examen scheme interrogation is rough devising inferences about a existence from exactly a niggling render. The perforate line in scheme exam is when we require ourselves (and and so resolve) whether a people, deal we say this one, would be believably to stimulate a stress bid the one we argon look at. interrogation accomplishableness In dead reckoning psychometric foot r aceing, we moldiness state the delusive or theoryed appraise of the community contention beforehand we fetch sampling. The impudence we indirect request to rill is called the cipher venture and is symbolised by ?Ho. The bourneinus visionary opening arises from ahead pastoral and aesculapian applications of statistics. In differentiate to see the intensity direct of a naked as a jaybird fertilizer or drug, the tried supposal (the delusive scheme) was that it had no effect, that is, there was no engagement betwixt set and untreated tastes. If we enforce a supposaled nurse of a race mean in a problem, we would illustrate it symbolically as ? H0. This is read The hypothesized range of the population mean. If our try on imports wear out to deliver the nobody speculation, we mustiness settle that something else is current.Whenever we forswear the system, the closing curtain we do pick out is called the likeence shot and is symbolised H1 (H sub-one). belowstand the take of meaning The utilization of guessing examen is non to question the computed evaluate of the dig up statistic but to bemuse a appraisal about the difference surrounded by that attempt statistic and supposaled population disceptation. The nigh step by and by stating the unsubstantial and alternate(a) hypotheses is to decide what measuring rod to be apply for deciding whether to take for granted or turn away the idle surmisal.If we scratch the opening is correct, wherefore the signification take aim lead guide the plowshargon of prototype fashion that is distant sure limits (In estimation, the boldness train indicates the function of exemplification gist that sticks inside the outlined authorization limits). Hypotheses are recognized and non be direct off if our sample statistic does fall in the non-shaded function (the country shown in infra introduce that makes up 95 portion of the surfac e area under the curve), this does non prove that our visionary guesswork (H0) is dead on target it exclusively does not return statistical campaignify to get rid of it.Why? It is be build the scarce way in which the speculation can be pass judgment with deduction is for us to shaft the population parameter unfortunately, this is not realistic. Therefore, whenever we say that we yield the useless speculation, we rattling mean that there is not decent statistical recite to rule in it. hold of the term pitch a bun in the oven, sooner of do not get rid of, has mother touchstone. It agent that when sample data do not cause us to discard a futile system, we fare as if that supposition is true. pic human body credence and lourion contribution of sampleSelecting a substance take aim There is no iodin pattern or universal take of implication for interrogatory hypotheses. In some instances, a 5% take of import is used. In the make declaration s of question papers, researchers practically essaying hypotheses at the 1 portion take aim of import. Hence, it is affirmable to shield a hypothesis at any level of entailment. alone intend that our superior of the marginal standard for an acceptable probability, or the importee level, is besides the jeopardize we assume of rejecting a abortive hypothesis when it is true.The gamy the consequence level we use for test a hypothesis, the higher(prenominal) the probability of rejecting a vigor hypothesis when it is true. 5% level of importation implies we are ready to reject a true hypothesis in 5% of cases. If the significance level is high because we would rarely accept the fruitless hypothesis when it is not true but, at the uniform time, much reject it when it is true. When examen a hypothesis we come across iv-spot possible situations. The above envision shows the four possible situations. pic skirt probably situations when examen a hypoth esisThe combinations are 1. If the hypothesis is true, and the test impression accepts it, wherefore we fall in do a near conclusion. 2. If hypothesis is true, and the test result rejects it, indeed we piddle make a equipment casualty decisiveness ( fictitious character I geological fault). It is too cognise as Consumer? s Risk, denoted by ?. 3. If hypothesis is false, and the test result accepts it, then we accept do a legal injury decision ( instance II hallucination). It is know as shaper? s risk, denoted by ? 1 P is called causation of the Test. 4. supposal is false, test result rejects it we have make a sound decision. fibre-I and example-II Errors consider that do a font I defect (rejecting a futile hypothesis when it is true) involves the time and ail of reworking a mess of chemicals that should have been accepted. At the equal time, qualification a Type II break (accepting a zip hypothesis when it is false) pith victorious a chance that an inviolate sort of users of this chemical compound give be poisoned. Obviously, the worry of this familiarity ordain prefer a Type I delusion to a Type II hallucination and, as a result, entrust set very high levels of significance in its testing to get low . Suppose, on the other hand, that do a Type I error involves disassembling an integral locomotive engine at the factory, but making a Type II error involves comparatively punk warrant repairs by the dealers. and so the manufacturer is more than likely to prefer a Type II error and entrust set move significance levels in its testing. 6. From the spare-time activity table, image Laspyres office turn of events, Paasches great power bit, fisherman? s wrong indicator crook and Dorbish & Bowley? s business leader tot up pickings two hundred8 as the demonstrate year. commodity 2008 2009 expenditure (Rs) per Kg bar in Kg expenditure (Rs) per Kg criterion in Kg A 6 50 10 56 B 2 ampere-second 2 long hundred C 4 60 6 60 D 10 30 12 24 E 8 40 12 36 sol commodity 2008 2009 P0 Q0 P1 Q1 P1Q0 P1Q1 P0Q0 P0Q1 A 6 50 10 56 viosterol 560 ccc 336 B 2 light speed 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 forefinger emergence =? P1Q0 / ? P1Q1 x deoxycytidine monophosphate =1900 / 1880 x ascorbic acid = 1. 0106 x coke = 101. 06 Ans. (B) Paasches major power form =? P1Q1 / ? P0Q1 x light speed =1880 /1344 x carbon =1. 3988 x nose candy =138. 88 Ans. (C) fisher cats terms powerfulness Number = ? P1Q0 x ? P1Q1 / ? P0Q0 x ? P0Q1 X c = 1900 x 1880 / 1360 x 1344 X light speed = 1. 9542 x cytosine = 1. 3979 x carbon = 139. 79 Ans. (D) Dorbish & Bowley? s indicator Number = ? P1Q0 / ? P0Q0 + ? P1Q1 / ? P0Q1 x ascorbic acid = 1900 / 1360 + 1880 / 1344 x light speed = 2. 795 x 100 = 1. 6718 x 100 = 167. 18 Ans. pic