Smu I Sem Stat Assignments Set 2

rMBA SEMESTER 1 MB0040 STATISTICS FOR MANAGEMENT- 4 attribute (Book ID B1129) Assignment Set- 1 (60 Marks) Note Each question carries 10 Marks. resoluteness all the questions 1. What do you mean by Statistical view? enjoin between Questionnaire and Schedule. ANS Definition of statistical survey A Statistical survey is a scientific process of collection and analysis of numerical data. Statistical surveys atomic number 18 used to collect numerical development about units in a tribe. opinions involve asking questions to individuals. Surveys of human creations be common in government, health, social science and marketing sectors.Stages of Statistical Survey Statistical surveys be categorized into two stages mean and execution. The two giving stages of Statistical survey AS FOLLOWS pic Planning a Statistical Survey The relevance and accuracy of data obtained in a survey depends upon the thrill exercised in planning. A properly planned investigating can idle words to be st results with least(prenominal) cost and time. footprints involved in the planning stage atomic number 18 as fol depresseds Step 1 Nature of the riddle to be investigated should be clearly defined in an unambiguous manner. Step 2 Objectives of the investigation should be stated at the out get along.Objectives could be to reach certain estimates Establish a theory Verify an existing rumor Find relationship between characteristics Step 3 The scope of the investigation has to be do clear. The scope of investigation refers to the argona to be covered, appellation of units to be studied, nature of characteristics to be observed, accuracy of measurements, analytical methods, time, cost and otherwise resources required. Step 4 Whether to use data collected from primary or secondary source should be determined in advance.Step 5 the memorial tablet of investigation is the final step in the process. It encompasses the determination of the number of investigators required, thei r training, supervision work needed, funds required. Execution of Statistical survey Control methods should be adopted at every stage of carrying out the investigation to understand 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 carefully and systematically analysed and interpreted.Differentiate between Questionnaire and Schedule Questionnaires contain simple questions and are filled by respondents. Schedules also contain questions but responses are put down directly by the investigator. 2. The table shows the data of Expenditure of a family on food, clothing, education, rent and other items. Depict the data shown in the table utilize Pie chart. Items Expenditure Food 4ccc Clothing one hundred twenty0 Education 700 Rent 2000 Others 600 ANS pic chassis Pie-chart showing expenditure of a family on various items 3. Average burthe n of c screws in knock A is 10. 4 gms. It is mixed with one hundred fifty screws of box B. Average weight of mixed screws is 10. 9 gms. Find the honest weight of screws of box B. ANS GIVEN THAT n1= light speed, n2 = cl, X1 = 10. 4 Gms, pic= 10. 9 Gms, X2 =? WE neck THAT pic 10. 9 = ( vitamin C*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 average weight of screws of box B is 11. 23 gms. 4. (a) Discuss the rules of fortune. (b) What is meant by Conditional Probability? ANS 1. Addition rule The addition rule of fortune states that i) If A and B are any two results then the probability of the feature of any A or B is given by pic ii) If A and B are two inversely exclusive events then the probability of circumstance of either A or B is given by pic ii) If A, B and C are any three events then the probability of happening of either A or B or C is given by pic In terms of Venn diagram, from the externalize 5. 4, we can draw a bead on 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 independent 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 conjure to know the probability that the price of a particular petroleum overlap will rise, given that the finance minister has increased the petrol price. such probabilities are known as conditional probabi lities.Thus the conditional probability of occurrence of an event A given that the event B has already occurred is de noned by P (A / B). Here, A and B are dependent events. Therefore, we birth the pursuance 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, thither 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 shot examination?Give Examples (b) Differentiate between reference-I and Type-II Errors ANS conjecture Testing Hypothesis proveing is about making inferences about a population from only a small sample. The bottom line in surmise testing is when we ask ourselves (and then decide) whether a population, like we think this one, would be likely to produce a sample like the one we are looking at. Testing Hypothesis In dead reckoning te sting, we must state the assumed or hypothesised value of the population parameter before we approach sampling. The assumption we wish to test is called the deceitful hypothesis and is symbolised by ?Ho. The term trifling hypothesis arises from earlier agricultural and medical applications of statistics. In order to test the effectiveness of a new fertiliser or drug, the tested hypothesis (the vigour hypothesis) was that it had no effect, that is, there was no disagreement between treated and untreated samples. If we use a hypothesised value of a population mean in a problem, we would represent it symbolically as ? H0. This is read The hypothesized value of the population mean. If our sample results fail to support the delusive hypothesis, we must conclude that something else is true.Whenever we deny the hypothesis, the conclusion we do accept is called the substitute(a) hypothesis and is symbolised H1 (H sub-one). Interpreting the take aim of significance The purpose of h ypothesis testing is not to question the computed value of the sample statistic but to set up a judgment about the difference between that sample statistic and hypothesised population parameter. The next step after stating the abortive and alternative hypotheses is to decide what cadence to be used for deciding whether to accept or reject the null hypothesis.If we assume the hypothesis is correct, then the significance aim will certify the percentage of sample means that is outside certain limits (In estimation, the assumption level indicates the percentage of sample means that glitters within the defined confidence limits). Hypotheses are accepted and not proved Even if our sample statistic does fall in the non-shaded region (the region shown in below figure that makes up 95 percent of the area under the curve), this does not prove that our null hypothesis (H0) is true it simply does not provide statistical evidence 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, kinda of do not reject, has become standard. It means that when sample data do not cause us to reject a null hypothesis, we expect as if that hypothesis is true. pic fig Acceptance and rejection region of sampleSelecting a entailment Level There is no single standard or prevalent level of significance for testing hypotheses. In some instances, a 5% level of significance is used. In the published results of research papers, researchers often 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 prime(prenominal) of the minimum standard for an acceptable probability, or the significance level, is als o the stake we assume of rejecting a null hypothesis when it is true.The higher 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 right decision. 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 error). It is known as producer? s risk, denoted by ? 1 P is called power of the Test. 4. Hypothesis is false, test result rejects it we have made a right decision. Type-I and Type-II Errors surmise that making a Type I error (rejecting a null hypothesis when it is true) involves the time and trouble of reworking a batch 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 taking a chance that an integral group of users of this chemical compound will be poisoned. Obviously, the management of this family will prefer a Type I error to a Type II error and, as a result, will set very high levels of significance in its testing to get low . Suppose, on the other hand, that making a Type I error involves disassembling an entire engine at the factory, but making a Type II error involves relatively inexpensive warranty repairs by the dealers. so the manufacturer is more likel y to prefer a Type II error and will set lower significance levels in its testing. 6. From the future(a) table, calculate Laspyres superpower function, Paasches indicator Number, Fisher? s charge index Number and Dorbish & Bowley? s Index Number taking 2008 as the immoral year. Commodity 2008 2009 Price (Rs) per Kg Quantity in Kg Price (Rs) per Kg Quantity in Kg A 6 50 10 56 B 2 100 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 2 100 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 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