Smu I Sem Stat Assignments Set 2

rMBA SEMESTER 1 MB0040 STATISTICS FOR MANAGEMENT- 4 Credits (Book ID B1129) Assignment Set- 1 (60 Marks) differentiate Each question carries 10 Marks. Answer all the questions 1. What do you imply by Statistical value? Differentiate among Questionnaire and Schedule. ANS Definition of statistical work A Statistical survey is a scientific process of cacheion and analysis of numerical info. Statistical surveys be go ford to collect numerical information about units in a population. aspects involve asking questions to individuals. Surveys of human populations are putting green in government, health, social science and marketing sectors.Stages of Statistical Survey Statistical surveys are categorized into cardinal stages planning and execution. The ii broad stages of Statistical survey AS FOLLOWS pic Planning a Statistical Survey The relevance and accuracy of data obtained in a survey depends upon the care exercised in planning. A justly planned investigating can lead to best results with least cost and time. Steps involved in the planning stage are as follows Step 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 statement chance upon relationship between characteristics Step 3 The scope of the investigation has to be made clear. The scope of investigation refers to the welkin to be covered, identification of units to be studied, nature of characteristics to be observed, accuracy of measurements, analytical methods, time, cost and another(prenominal) resources required. Step 4 Whether to use data collected from primary or secondary source should be determined in advance.Step 5 the organization of investigation is the final look in the process. It encompasses the determination of the add together of investigators required, their training, supe rvision work needed, funds required. Execution of Statistical survey Control methods should be adopted at every stage of carrying out the investigation to check 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 alter by respondents. Schedules also contain questions entirely responses are recorded 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 utilise Pie chart. Items Expenditure Food 4300 Clothing 1200 Education 700 Rent 2000 Others 600 ANS pic Fig Pie-chart showing expenditure of a family on various items 3. Average weight of coulomb screws in street corner A is 10. 4 gms. It is immix with one hundred fifty screws of box B. Average weight of mixed screws is 10. 9 gms. Find the average weight of screws of box B. ANS GIVEN THAT n1= deoxycytidine monophosphate, n2 = 150, X1 = 10. 4 Gms, pic= 10. 9 Gms, X2 =? WE KNOW THAT pic 10. 9 = ( one hundred*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 Probability. (b) What is meant by Conditional Probability? ANS 1. Addition rule The gain rule of fortune states that i) If A and B are any two events thence the luck of the detail of all A or B is precondition by pic ii) If A and B are two mutually exclusive events then the probability of item of either A or B is habituated by pic ii) If A, B and C are any three events then the probability of occurrence of either A or B or C is given by pic In te rms of Venn diagram, from the head 5. 4, we can calculate 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 wish to live the probability that the price of a particular petroleum product will rise, given that the finance subgenus Pastor has increased the petrol price. Such probabilities are known as conditional probabilities.Thus the condit ional 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 be in possession of 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 bare(a) 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 supposal Testing?Give Examples (b) Differentiate between pillowcase-I and event-II Errors ANS possibility Testing hypothesis interrogatory is about making inferences about a population from only a small sample. The rear end line in hypothesis footraceing 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 hypothesi s testing, we must state the assumed or hypothesised value of the population parameter forwards we begin sampling. The assumption we wish to test is called the unsubstantial hypothesis and is symbolised by ?Ho. The term invalid hypothesis arises from earlier agricultural and medical applications of statistics. In order to test the effectiveness of a smart fertiliser or drug, the tested hypothesis (the null hypothesis) was that it had no effect, that is, there was no difference 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 null hypothesis, we must conclude that something else is true.Whenever we resist the hypothesis, the conclusion we do accept is called the alternative hypothesis and is symbolised H1 (H sub-one). translation the direct of substance The purpose of hypothes is testing is not to question the computed value of the sample statistic but to make a judgment 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 criterion to be used for deciding whether to accept or reject the null hypothesis.If we assume the hypothesis is correct, then the meaning level will indicate the pct of sample means that is outside certain limits (In estimation, the confidence level indicates the percentage of sample means that water determine 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 acc epted with proof 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, instead of do not reject, has become standard. It means that when sample data do not cause us to reject a null hypothesis, we behave as if that hypothesis is true. pic fig Acceptance and rejection region of sampleSelecting a importation Level There is no single standard or universal level of significance for testing hypotheses. In some instances, a 5% level of significance is used. In the published results of research papers, researchers lots 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 choice 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 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 alike time, often reject it when it is true. When testing a hypothesis we come across four possible situations. The in a higher place 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 conclusiveness. 2. If hypothesis is true, and the test result rejects it, then we have made a wrong decision ( grammatical case I mistake). 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 wro ng 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 Suppose 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 pickings a chance that an entire group of users of this chemical compound will 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 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. Then the manufacturer is more likely to prefer a Type II error and will set lower significance levels in its testing. 6. From the following table, calculate Laspyres major power matter, Paasches Index Number, Fisher? s bell Index Number and Dorbish & Bowley? s Index Number taking 2008 as the base 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 1 00 = 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