STATISTICS FOR MANAGEMENT
Credits (Book ID: B1129) Assignment Set- 1 (60 Marks) Note: Each topic carries 10 Marks. Answer all the topics 1. What do you moderation by Statistical Survey? Differentiate among “Questionnaire” and “Schedule”. ANS: Definition of statistical reconnoitre: A Statistical reconnoitre is a philosophical way of store and resolution of numerical grounds. Statistical reconnoitres are used to accumulate numerical apprehendledge encircling units in a population. Surveys mingle interrogation topics to men-folks. Surveys of civilized populations are despicable in empire, soundness, collective inferiorstanding and marketing sectors.
Stages of Statistical Survey: Statistical reconnoitres are categorized into two positions – planning and project. The two ample positions of Statistical reconnoitre AS FOLLOWS: [pic] Planning a Statistical Survey: The intercourse and faultlessness of grounds obtained in a reconnoitre depends upon the foresight exercised in planning. A fitly scoped search can control to best conclusions delay balanceest require and occasion. Steps mingled in the planning position are as follows: Tlearn 1: Naturalness of the quantity to be investigated should be evidently defined in an plain habit. Tlearn 2: Objectives of the search should be normal at the exordium.
Objectives could be to:
Obtain real estimates
Establish a theory
Verify an existing narratement
Find intercommunity among characteristics
Step 3: The design of the search has to be made manifest. The design of search refers to the area to be covered, identification of units to be thoughtful, naturalness of characteristics to be observed, faultlessness of measurements, analytical methods, occasion, require and other resources required. Tlearn 4: Whether to use grounds accumulateed from pristine or subordinate fount should be rooted in track.
Step 5: the construction of search is the conclusive tlearn in the way. It encompasses the gratification of the compute of investigators required, their inoculation, supervision issue needed, funds required. Project of Statistical reconnoitre: Control methods should be adopted at perfect position of carrying out the search to control the faultlessness, coverage, methods of measurements, resolution and explanation. The accumulateed grounds should be edited, classified, tabulated and presented in diagrams and graphs. The grounds should be foresightfully and regularly analysed and interpreted.
Differentiate among “Questionnaire” and “Schedule”: Questionnaires hold unqualified topics and are filled by respondents. Schedules besides hold topics but responses are recitative at-once by the investigator.
The consultation shows the grounds of Appraisement of a nativity on assistance, investment, direction, schism and other items. Depict the grounds shown in the consultation using Pie chart.
ANS: [pic] Fig: Pie-chart showing appraisement of a nativity on diverse items
Average gravity of 100 screws in box A is 10. 4 gms. It is qualified delay 150 screws of box B. Balance gravity of qualified screws is 10. 9 gms. Find the balance gravity of screws of box B. ANS: GIVEN THAT:
n2 = 150,
X1 = 10. 4 Gms,
[pic]= 10. 9 Gms,
X2 =? WE KNOW THAT: [pic] 10. 9 = (100*10. 4) + (150 X2) / 100+150 10. 9 = 1040 + 150 X2 / 250 0. 9*250 = 1040 + 150 X2 2725 = 1040 + 150 X2 150 = 2725-1040 X2 =1685 / 150 X2 = 11. 23 Gms Therefore, the balance gravity of screws of box B is 11. 23 gms. Discuss the governments of “Probability”.
What is moderationt by “Conditional Probability”? ANS:
Addition government: The attention government of presumption narrates that: i) If ‘A’ and ‘B’ are any two facts then the presumption of the affair of either ‘A’ or ‘B’ is ardent by: [pic] ii) If ‘A’ and ‘B’ are two mutually odious facts then the presumption of affair of either A or B is ardent by: [pic] ii) If A, B and C are any three facts then the presumption of affair of either A or B or C is ardent by: [pic] In conditions of Venn diagram, from the type 5. 4, we can weigh the presumption of affair of either fact ‘A’ or fact ‘B’, ardent that fact ‘A’ and fact ‘B’ are trusting facts. From the type 5. 5, we can weigh the presumption of affair of either ‘A’ or ‘B’, ardent that, facts ‘A’ and ‘B’ are intrusting facts. From the type 5. 6, we can weigh the presumption of affair of either ‘A’ or ‘B’ or ‘C’, ardent that, facts ‘A’, ‘B’ and ‘C’ are trusting facts. pic] iv) If A1, A2, A3………, An are ‘n’ mutually odious and wasting facts then the presumption of affair of at balanceest one of them is ardent by: [pic] 2. Multiplication government: If ‘A’ and ‘B’ are two intrusting facts then the presumption of affair of ‘A’ and ‘B’ is ardent by: [pic] Unlawful Probability: Sometimes we eagerness to apprehend the presumption that the appraisement of a detail petroleum issue achieve fuse, ardent that the finance attend has increased the petrol appraisement. Such probabilities are apprehendn as unlawful probabilities.
Thus the unlawful presumption of affair of an fact ‘A’ ardent that the fact ‘B’ has alwilling occurred is denoted by P (A / B). Here, ‘A’ and ‘B’ are trusting facts. Therefore, we confirm the subjoined governments. If ‘A’ and ‘B’ are trusting facts, then the presumption of affair of ‘A and B’ is ardent by: [pic] It follows that: [pic] For any bivariate arrangement, there exists two ultimate arrangements and ‘m + n’ unlawful arrangements, where ‘m’ and ‘n’ are the compute of classifications/characteristics thoughtful on two variables.
What is moderationt by “Hypothesis Testing”?
Give Examples (b) Differentiate among “Type-I” and “Type-II” Errors ANS: Conjecture Testing: Conjecture trialing is encircling making inferences encircling a population from merely a insignificant specimen. The deep row in conjecture trialing is when we ask ourselves (and then determine) whether a population, apmake-trial-of we reckon this one, would be approvely to product a specimen apmake-trial-of the one we are looking at. Testing Hypothesis: In conjecture trialing, we must narrate the inconsequent or conjectureed appraise of the population parameter antecedently we arise sampling. The self-assertion we eagerness to trial is determined the void conjecture and is symbolised by ?
Ho”. The message void conjecture arises from precedent unroving and medical applications of statistics. In dispose to trial the efficiency of a new fertiliser or refuse, the trialed conjecture (the void conjecture) was that it had no issue, that is, there was no distinction among treated and untreated specimens. If we use a conjectureed appraise of a population moderation in a quantity, we would enact it symbolically as ? H0. This is learn - The hypothesized appraise of the population moderation. If our specimen conclusions trip to maintenance the void conjecture, we must deduce that bigwig else is penny.
Whenever we throw-by the conjecture, the misentry we do confirm is determined the cherished conjecture and is symbolised H1 (“H sub-one”). Interpreting the flatten of reason: The scope of conjecture trialing is not to topic the computed appraise of the specimen statistic but to frame a firmness encircling the distinction among that specimen statistic and conjectureed population parameter. The instant tlearn succeeding stating the void and cherished hypotheses is to determine what proof to be used for deciding whether to confirm or throw-by the void conjecture.
If we affect the conjecture is set-right, then the reason flatten achieve mark the percentage of specimen moderations that is after a whileout real limits (In mark, the faith flatten marks the percentage of specimen moderations that droops delayin the defined faith limits). Hypotheses are confirmed and not make-trial-ofd: Even if our specimen statistic does droop in the non-shaded country (the country shown in inferiorneath type that frames up 95 percent of the area inferior the deflexion), this does not make-trial-of that our void conjecture (H0) is penny; it merely does not contribute statistical exemplification to throw-by it.
Why? It is accordingly the merely way in which the conjecture can be confirmed delay realty is for us to apprehend the population parameter; unfortunately, this is not mitigated. Therefore, whenever we say that we confirm the void conjecture, we in-effect moderation that there is not tit statistical exemplification to throw-by it. Use of the message confirm, instead of do not throw-by, has behove model. It moderations that when specimen grounds do not source us to throw-by a void conjecture, we beconfirm as if that conjecture is penny. [pic] fig: Acceptance and throw-byion country of specimen
Selecting a Reason Level: There is no only model or total flatten of reason for trialing hypotheses. In some instances, a 5% flatten of reason is used. In the published conclusions of discovery papers, discoveryers frequently trial hypotheses at the 1 percent flatten of reason. Hence, it is mitigated to trial a conjecture at any flatten of reason. But retain that our cherished of the reserve model for an accepconsultation presumption, or the reason flatten, is besides the abandon we affect of throw-bying a void conjecture when it is penny.
The conspicuous the reason flatten we use for trialing a conjecture, the conspicuous the presumption of throw-bying a void conjecture when it is penny. 5% flatten of reason implies we are learny to throw-by a penny conjecture in 5% of cases. If the reason flatten is proud then we would rarely confirm the void conjecture when it is not penny but, at the corresponding occasion, frequently throw-by it when it is penny. When trialing a conjecture we succeed abutting lewd mitigated situations. The overhead type shows the lewd mitigated situations. [pic] Table: Mitigated situations when trialing a conjecture
The combinations are:
If the conjecture is penny, and the trial conclusion confirms it, then we confirm made a fit firmness.
If conjecture is penny, and the trial conclusion throw-bys it, then we confirm made a evil-doing firmness (Type I falsity). It is besides apprehendn as Consumer? s Risk, denoted by ?.
If conjecture is mock, and the trial conclusion confirms it, then we confirm made a evil-doing firmness (Type II falsity). It is apprehendn as productr? s abandon, denoted by ? 1 – P is determined dominion of the Test.
Hypothesis is mock, trial conclusion throw-bys it – we confirm made a fit firmness. Type-I” and “Type-II” Errors: Suppose that making a Type I falsity (rejecting a void conjecture when it is penny) mingles the occasion and labor of reworking a conspire of chemicals that should confirm been confirmed. At the corresponding occasion, making a Type II falsity (accepting a void conjecture when it is mock) moderations initiative a casualty that an total clump of users of this chemical junction achieve be poisoned. Obviously, the skillful-treatment of this crew achieve advance a Type I falsity to a Type II falsity and, as a conclusion, achieve set very proud flattens of reason in its trialing to get low ?? . Suppose, on the other index, that making a Type I falsity mingles disassembling an total engine at the factory, but making a Type II falsity mingles relatively worthless defence repairs by the dealers. Then the creator is over approvely to advance a Type II falsity and achieve set inferior reason flattens in its trialing. 6. From the subjoined consultation, weigh Laspyres Index Number, Paasches Index Number, Fisher? s Appraisement Index Compute and Dorbish & Bowley? s Index Compute initiative 2008 as the deep year.