Smu I Sem Stat Assignments Set 2

rMBA SEMESTER 1 MB0040 STATISTICS FOR MANAGEMENT- 4 assign (Book ID B1129) Assignment Set- 1 (60 Marks) Note from each hotshot question carries 10 Marks. Answer totally the questions 1. What do you mean by statistical Survey? Differentiate between Questionnaire and memorial. autonomic nervous system Definition of statistical study A statistical survey is a scientific process of collection and psychoanalysis of numerical information. Statistical surveys be employ to collect numerical information close to units in a universe of discourse. Surveys involve intercommunicate questions to individuals. Surveys of human cosmoss be common in government, health, social science and marketing sectors.Stages of Statistical Survey Statistical surveys ar categorized into deuce stages preparation and execution. The two full stages of Statistical survey AS FOLLOWS pic readying a Statistical Survey The relevance and accuracy of data obtained in a survey depends upon the care exerc ised in planning. A properly planned investigation shtup lead to best results with least scathe and time. flavours involved in the planning stage are as fol first gears pace 1 Nature of the problem to be investigated should be clearly defined in an unambiguous manner. Step 2 Objectives of the investigation should be stated at the outset.Objectives could be to Obtain certain estimates Establish a theory Verify an existing averment Find relationship between characteristics Step 3 The scope of the investigation has to be make clear. The scope of investigation refers to the demesne to be covered, identification of units to be studied, spirit of characteristics to be observed, accuracy of measurements, analytical methods, time, apostrophize and other resources required. Step 4 Whether to enforce data collected from primary or secondary source should be pertinacious in advance.Step 5 the organization of investigation is the final step in the process. It encompasses the h abituate of the number of investigators required, their training, supervision work needed, pecuniary resource required. Execution of Statistical survey get word methods should be adopted at every(prenominal) stage of carrying out the investigation to infract the accuracy, coverage, methods of measurements, analysis and interpretation. The collected data should be edited, classified, tabulated and presented in diagrams and graphs. The data should be cautiously and systematically analysed and interpreted.Differentiate between Questionnaire and Schedule Questionnaires withdraw simple questions and are filled by respondents. Schedules also contain questions but responses are recorded directly by the investigator. 2. The display board shows the data of disbursal of a family on food, clothing, education, rent and other items. Depict the data shown in the table using Pie chart. Items Expenditure Food 4300 Clothing one hundred twenty0 Education 700 tide rip 2000 Others 600 au tonomic nervous system pic Fig Pie-chart showing expense of a family on various items 3. total metric weight unit of atomic number 6 screws in blow A is 10. 4 gms. It is tangled with cl screws of recess B. Average weight of mixed screws is 10. 9 gms. Find the average weight of screws of box B. ANS GIVEN THAT n1= hundred, n2 = cl, X1 = 10. 4 Gms, pic= 10. 9 Gms, X2 =? WE KNOW THAT pic 10. 9 = ( vitamin C*10. 4) + (150 X2) / cytosine+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 average weight of screws of box B is 11. 23 gms. 4. (a) Discuss the draw reins of prospect. (b) What is meant by Conditional Probability? ANS 1. Addition harness The addition rule of luck states that i) If A and B are whatsoever two events in that respectfore the fortune of the position of every A or B is give up by pic ii) If A and B are two mutually exclusive events consequently the fortu ne of natural event of either A or B is habituated by pic ii) If A, B and C are any three events then the hazard of occurrence of either A or B or C is prone by pic In terminations of Venn diagram, from the betoken 5. 4, we can inscribe the probability of occurrence of either event A or event B, given that event A and event B are dependent events. From the figure 5. 5, we can calculate the probability of occurrence of either A or B, given that, events A and B are free lance events. From the figure 5. 6, we can calculate the probability of occurrence of either A or B or C, given that, events A, B and C are dependent events. pic iv) If A1, A2, A3, An are n mutually exclusive and exhaustive events then the probability of occurrence of at least one of them is given by pic 2. Multiplication rule If A and B are two independent events then the probability of occurrence of A and B is given by pic Conditional Probability Sometimes we lack to know the probability that the price of a particular petroleum product volition rise, given that the finance minister has change magnitude the petrol price. Such probabilities are cognize as conditional probabilities.Thus the conditional probability of occurrence of an event A given that the event B has already occurred is denoted by P (A / B). Here, A and B are dependent events. Therefore, we bemuse the following rules. If A and B are dependent events, then the probability of occurrence of A and B is given by pic It follows that pic For any bivariate distribution, there exists two marginal distributions and m + n conditional distributions, where m and n are the number of classifications/characteristics studied on two variables. 5. (a) What is meant by Hypothesis judge?Give Ex international ampereles (b) Differentiate between Type-I and Type-II Errors ANS Hypothesis exam Hypothesis examination is about fashioning inferences about a population from only a pure savour. The bottom line in possible action interrogat ion is when we ask ourselves (and then decide) whether a population, handle we think this one, would be probable to produce a prototype like the one we are looking at. Testing Hypothesis In guess shielding, we mustiness state the confiscated or supposaled prize of the population parameter before we arrest sampling. The assumption we wish to raise is called the trifling theory and is symbolised by ?Ho. The term zilch hypothesis arises from earlier awkward and medical applications of statistics. In order to test the effectiveness of a new plant food or drug, the tested hypothesis (the zipper hypothesis) was that it had no effect, that is, there was no fight between treated and untreated attempts. If we use a hypothesised revalue of a population mean in a problem, we would comprise it symbolically as ? H0. This is read The hypothesized value of the population mean. If our sample results fail to substitute the null hypothesis, we must conclude that something else is true.Whenever we protest the hypothesis, the conclusion we do ware is called the alternating(a) hypothesis and is symbolised H1 (H sub-one). Interpreting the take of logical implication The purpose of hypothesis interrogatory is not to question the computed value of the sample statistic but to make a image about the difference between that sample statistic and hypothesised population parameter. The next step after stating the null and alternative hypotheses is to decide what amount to be used for deciding whether to abide or eradicate the null hypothesis.If we attain the hypothesis is correct, then the significance take get out indicate the partage of sample actor that is outside certain limits (In estimation, the corporate trust take indicates the percentage of sample marrow that falls within the defined federal agency limits). Hypotheses are authoritative and not spread out Even if our sample statistic does fall in the non-shaded region (the region shown in on a inflict floor figure that makes up 95 percent of the area under the curve), this does not prove that our null hypothesis (H0) is true it just now does not provide statistical exhibit to reject it.Why? It is because the only way in which the hypothesis can be accepted with certainty is for us to know the population parameter unfortunately, this is not possible. Therefore, whenever we say that we accept the null hypothesis, we actually mean that there is not sufficient statistical evidence to reject it. Use of the term accept, sort of of do not reject, has become standard. It fashion that when sample data do not cause us to reject a null hypothesis, we be put up as if that hypothesis is true. pic fig Acceptance and rejection region of sampleSelecting a Significance Level There is no single standard or oecumenic level of significance for exam hypotheses. In some instances, a 5% level of significance is used. In the published results of look into papers, researchers oft en test hypotheses at the 1 percent level of significance. Hence, it is possible to test a hypothesis at any level of significance. But remember that our option of the minimum standard for an acceptable probability, or the significance level, is also the risk we assume of rejecting a null hypothesis when it is true.The laid-back the significance level we use for testing a hypothesis, the higher the probability of rejecting a null hypothesis when it is true. 5% level of significance implies we are ready to reject a true hypothesis in 5% of cases. If the significance level is high then we would rarely accept the null hypothesis when it is not true but, at the same time, often reject it when it is true. When testing a hypothesis we come across four possible situations. The above figure shows the four possible situations. pic Table possible situations when testing a hypothesisThe combinations are 1. If the hypothesis is true, and the test result accepts it, then we have made a righ t finding. 2. If hypothesis is true, and the test result rejects it, then we have made a wrong decision (Type I fracture). It is also known as Consumer? s Risk, denoted by ?. 3. If hypothesis is false, and the test result accepts it, then we have made a wrong decision (Type II break). It is known as producer? s risk, denoted by ? 1 P is called might of the Test. 4. Hypothesis is false, test result rejects it we have made a right decision. Type-I and Type-II Errors order that do a Type I error (rejecting a null hypothesis when it is true) involves the time and trouble of reworking a smokestack of chemicals that should have been accepted. At the same time, making a Type II error (accepting a null hypothesis when it is false) means winning a chance that an good group of users of this chemical compound give be poisoned. Obviously, the management of this company will prefer a Type I error to a Type II error and, as a result, will set very high levels of significance in its te sting to get low ?? . Suppose, on the other hand, that making a Type I error involves disassembling an undefiled engine at the factory, but making a Type II error involves relatively inexpensive warranty repairs by the dealers. Then the manufacturer is more in all likelihood to prefer a Type II error and will set lower significance levels in its testing. 6. From the following table, calculate Laspyres office bod, Paasches Index keep down, fisher cat? s outlay Index trope and Dorbish & Bowley? s Index Number taking 2008 as the base year. trade good 2008 2009 Price (Rs) per Kg Quantity in Kg Price (Rs) per Kg Quantity in Kg A 6 50 10 56 B 2 one C 2 120 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 56 500 560 300 336 B 2 snow 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= ?P0 Q1= 1880 1360 1344 (A) Laspyres Index Number =? P1Q0 / ? P1Q1 x 100 =1900 / 1880 x 100 = 1. 0106 x 100 = 101. 06 Ans. (B) Paasches Index Number =? P1Q1 / ? P0Q1 x 100 =1880 /1344 x 100 =1. 3988 x 100 =138. 88 Ans. (C) Fishers Price Index Number = ? P1Q0 x ? P1Q1 / ? P0Q0 x ? P0Q1 X 100 = 1900 x 1880 / 1360 x 1344 X 100 = 1. 9542 x 100 = 1. 3979 x 100 = 139. 79 Ans. (D) Dorbish & Bowley? s Index Number = ? P1Q0 / ? P0Q0 + ? P1Q1 / ? P0Q1 x 100 = 1900 / 1360 + 1880 / 1344 x 100 = 2. 795 x 100 = 1. 6718 x 100 = 167. 18 Ans. pic