Smu I Sem Stat Assignments Set 2

rMBA SEMESTER 1 MB0040 – STATISTICS FOR MANAGEMENT- 4 Credits (Book ID: B1129) Assignment Set- 1 (60 Marks) Note: Each question carries 10 Marks. Answer all the questions 1. What do you mean by Statistical Survey? Differentiate between â€Å"Questionnaire† and â€Å"Schedule†. ANS: Definition of statistical survey: A Statistical survey is a scientific process of collection and analysis of numerical data. Statistical surveys are used to collect numerical information about units in a population. Surveys involve asking questions to individuals. Surveys of human populations are common in government, health, social science and marketing sectors.Stages of Statistical Survey: Statistical surveys are categorized into two stages – planning and execution. The two 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 properly planned in vestigation 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 †¢ Find relationship between characteristics Step 3: The scope of the investigation has to be made clear. The scope of investigation refers to the area to be covered, identification of units to be studied, nature of characteristics to be observed, accuracy of measurements, analytical methods, time, cost and other 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 step in the process. It encompasses the determination of the number of investigators requi red, their training, supervision 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 â€Å"Questionnaire† and â€Å"Schedule†: Questionnaires contain simple questions and are filled by respondents. Schedules also contain questions but 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 using 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 var ious items 3. Average weight of 100 screws in box A is 10. 4 gms. It is mixed with 150 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=100, †¢ 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 average weight of screws of box B is 11. 23 gms. 4. (a) Discuss the rules of â€Å"Probability†. (b) What is meant by â€Å"Conditional Probability†? ANS: 1. Addition rule: The addition rule of probability states that: i) If ‘A’ and ‘B’ are any two events then the probability of the occurrence of either ‘A’ or ‘B’ is given by: [pic] ii) If ‘A’ and ‘B’ are two mutually exclusive events then the pro bability of occurrence of either A or B is given 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 terms of Venn diagram, from the figure 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†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦, An are ‘n’ mutually exclusive and exhaustive events then the probability of occurrence of at le ast 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 know the probability that the price of a particular petroleum product will rise, given that the finance minister has increased the petrol price. Such probabilities are known 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 have 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 + nâ€⠄¢ conditional distributions, where ‘m’ and ‘n’ are the number of classifications/characteristics studied on two variables. 5. (a) What is meant by â€Å"Hypothesis Testing†?Give Examples (b) Differentiate between â€Å"Type-I† and â€Å"Type-II† Errors ANS: Hypothesis Testing: Hypothesis testing is about making inferences about a population from only a small sample. The bottom line in hypothesis 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 hypothesis testing, we must state the assumed or hypothesised value of the population parameter before we begin sampling. The assumption we wish to test is called the null hypothesis and is symbolised by ?Ho†. The term null hypothesis arises from earlier agricultural and medical applications of statistics. In order to test the effectiveness of a new fert iliser 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 reject the hypothesis, the conclusion we do accept is called the alternative hypothesis and is symbolised H1 (â€Å"H sub-one†). Interpreting the level of significance: The purpose of hypothesis 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 hypot hesis.If we assume the hypothesis is correct, then the significance level will indicate the percentage of sample means that is outside certain limits (In estimation, the confidence level indicates the percentage of sample means that falls 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, instead of do not reject, has become standard. It means that when samp le 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 Significance 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 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 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 nu ll 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 error). 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 â€Å"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 taking 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 Index Number, Paasches Index Number, Fisher? s Price 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) Fisher’s 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]

A Research On Native Americans: Origin, Culture, Way Of Life And Contribution To The United States

The origin and presence of Native Americans in the Western Hemisphere has been one of the most debatable issues in both American and world historical studies. European invaders entering the new land were quite challenged to find about 100 million inhabitants in the Americas; a land they had always presumed was vast and vacant.These European settlers as well as scientists believed that the American natives belonged to the biblical Lost Tribes of the nation of Israel, while others fancifully argued that these natives could have been the remnant of lost civilizations such as Mu or Atlantis.Early European settlers insisted that Native Americans must have had their origin in ancient Israel, Rome, the Irish, Welsh or Viking lands. Scientists have however changed their perspective over recent times and joined Native American voices to support the notion that these people are indigenous to the Americas.Tied into the issue of native origin are legal standings regarding Native sovereignty, pos session of sacred artifacts and Native remains, Native American spokesman-ship or representation, as well as the rules that should be used to analyze the evidence deduced from history and science about their indigenous status in this land (Carliste & Golson 2006, p.1).Native Americans in the United StatesHistorically, the earliest Native tribes to inhabit the Americas are the Athapascans and Inuits who are believed to have entered the land through the Bering Strait that connects Alaska and Siberia. Others are said to have traveled by boat or canoe around the North American Pacific coast and Arctic Circle to predominate North America and parts of South America.But the Native American people have together with others. Always questioned the Bering Strait theory and gone ahead to insist that they have inhabited the Americas as far back as their origin can be traced.Researchers into the origins of Native Americans have suggested that these people could have entered the Americas through m ultiple migrations not only by the land bridge or boat at the Bering Strait; but also through sea from Polynesia and parts of Europe.Genetic evidence has also come up with suggestions that Native Americans had already arrived in the Americas about 15,000 to 30,000 years long before the Bering Strait had been exposed by lowering sea levels. Recent discoveries have found genetic evidence of Polynesian origin among five Native tribes like the Mapuche, Cayapa of Ecuador, Huilleche, Nuu-Chal-Nulth in Canada, and the Atacameno of Chile.Native oral traditions tell about a journey to the Americas by boat and the present-day continent popularly referred to as the United States of America is an ancestral home to over 500 Indian nations. The state of California alone was home to over 60 tribes of between 30,000 – 40,000 Native people before the early European invasion (Stubben & Sokolow 2005, p.1-3; Carliste & Golson 2006, p.1-6).Native American tribes spoke a variety of languages but m ost of the northeastern tribes lived in semi-permanent and permanent dwellings, socially organized under clan membership.The clans were matrilineal and young men were raised in the households of their mothers by their maternal uncles. Daily Native American life revolved around hunting, gathering, farming and fishing, the main crops being maize, beans and squash.Native Americans moved in groups of about 50 – 100 people because such a group could manage reasonable hunting exploits especially when hunting large buffalo herds. Family was very important to the Native Americans and all members of a family ranging from grandparents, parents and the children shared a very special bond. Family and tribal elders were highly respected and their decisions in various matters were crucial to the existence of a clan or entire tribe.Men did the hunting and took care of other tribal matters such as maintenance of tribal boundaries while the women provide labor for tilling the fields as well a s doing several other chores. In some tribes like the Iroquois, women also held powerful positions whereby they controlled the election and removal of clan chiefs.These gender based cultural traits were to create a lot of cross-cultural conflict when the European arrived in the Americas (Stubben & Sokolow 2005, p.57; Carliste & Golson 2006, p.113).Life for the Native Americans however changed drastically with the arrival of European settlers to America especially during the early 1800s, when the Americas experienced an influx of European settlers.The need to supply the American nation with foodstuffs, clothing and lumber led to the displacement of Native people and immediately, plans got under way to resettle them to reservations. European invasion is said to have led to the extinct of some Native tribes like the Beothuk who are said to have been wiped out completely.Most other tribes lost over 90% of their people to European genocide because the white settlers had better weapons of warfare that were also more extreme and violent than the native peoples could resist.In their conquests, European invaders murdered noncombatants as well as used biological warfare such as deliberate spread of disease and starvation. 75 million Indians are estimated to have died with some estimates going as high as 112 million (Pritzker 2000, p.162; Carliste & Golson 2006, p.9, 26).European settlement was detrimental to Native American existence because it disrupted every aspect of their lives. The relocation f Native tribes from their native lands disrupted their way of life.Between 1854 and 1855 for example, Washington governor Isaac I. Stevens signed four treaties in quick succession with the Waka Walla Cayuse, Yakima, Makah, Nez Perce, Lushootsedd and Coer d’ Alene Native tribes around the Oregon and Washington territories.Through these treaties, Native lands were ceded back to the government which included the choicest lands of Tacoma, Seattle and Olympia. In return, th ese tribes were allotted tracts of lands although the government held the right over waterways and public transportation throughout these territories.Although native tribes retained such rights as fishing, hunting and grazing rights, these allotments marked the beginning of a restricted lifestyle for the Native tribes.These treaties not only eroded native culture but their lifestyle as well, and forced their assimilation into reservations (Hoxie, Mancall & Merrell 2001, p. 67; Pritzer 2000, p. 5, 214; Carliste & Golson 2006, p.29, 75, 111).

Job Description Essay Example | Topics and Well Written Essays - 500 words

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Successional Planning Research Paper Example | Topics and Well Written Essays - 250 words

Successional Planning - Research Paper Example The organization provides services to the customer within the town of Quispamsis. The organization has more than 100 employees and has been in service for many years. It is managed by professionals who ensure continuity and expansion. Exploitation is evidences in the organization with some of the professional providing service being underpaid. Sometimes salary delay and over taxation are noticed. For improvement, the employee compensation policies should be reviewed. Individual should be compensated with respect to their education level and experience. Pension scheme should also be introduced in order to compensate people after retirement. Employees should be given medical and health insurance cover to compensate them in case of injury. Training should be held in order to make sure that the employees are conversant with the organization’s operations and strategies. The current state is good and the existing operational strategies should be maintained or improved. In future there should be skilled and motivated employees in order to increase the performance and gain more income. Human resource manager should consider hiring skilled employees and also motivate the existing employee in order to improve

Monopolies in Todays Market Essay Example | Topics and Well Written Essays - 2000 words

Monopolies in Todays Market - Essay Example Atimes, monopolies exist as a result of government backings in which case the monopolies provide goods, products or services which the government considers essential to the well being of the people. The absence of supply curve in the monopolized market causes inefficient allocation of society's resources. Therefore there is that tendency for a monopolist to charge high prices and probably making higher profits compared with firms in perfect competition. The objective of this paper is to unravel the role of monopolies in today's market and the implications of technology and systems on the monopolies. The rest of this paper examines different types of monopoly, its revenue, monopoly and price discriminations, and implications of technology and systems. (a) Pure Monopoly: This is a type of monopoly that exists in a particular region or city in which its products have no close substitutes. This makes it possible for the monopolist to charge extra prices because their products are necessities. (b) Natural Monopoly: A monopoly that exists because of economies of scale it enjoys in which large scale production brings lower average cost. Even though a competitor arises in the industry lower prices the monopolist would charge is capable of sending the competitor off the market. (c) Efficiency Monopoly: When government does not legalize monopoly, a monopoly may exist largely due to its ability to satisfy the customers in which case competition is inadvertently rule out. (d) Legal Monopoly: This form of monopoly has government backing such that laws are enacted to simply rule out competition. Wikipedia says "when such a monopoly is granted to a private party, it is a government granted monopoly; when it is operated by government itself, it is government monopoly or state monopoly". Monopoly Revenue Basically, a monopolist faces downward sloping demand curve which is also the firm's average revenue curve. As the monopolist sells a single price for its products, average revenue per product is the same as the price. For the monopolist to increase its sales it charges lower unit price for its products. At price P1 the monopolist only manages to sell Q1 quantity of the product; in order to increase its sales it reduces the price from P1 to P2 and as such sales is increased from Q1 to Q2 which he now gains in figure 1 below. Given the above scenario, the differential of the total revenue in relation to quantity gives marginal revenue which shows that the additional revenue large enough to offset the reduction in price. Figure 1: Showing Monopolist's gain brought about by price reduction. However, the monopolist maximizes profit where marginal revenue equals marginal cost. The reason is the since marginal cost is always greater than zero the monopolist will operate at profit because marginal revenue will be positive and where demand is elastic. If the monopolist stops production where marginal cost is less than marginal revenue, he will be leaving his profit untapped while quantity in which marginal revenue is greater than marginal cost the firm will be operating at losses. Profit maximizing price is determined by drawing a line where marginal co

Personal Statement Example | Topics and Well Written Essays - 750 words - 12

Personal Statement Example This is what I would like to be able to do. I consider myself to be highly competitive, always wanting to surpass what I have already achieved. I engage in healthy competition with my colleagues, but I am more focused on outdoing myself. I consider myself my toughest competition. During my early years in school and up to middle school, I have been an active student leader, working hard on my academics as well as the extracurricular activities. I desired not only to hit high marks in my subjects, but also be able to participate in school activities and hone my other skills. My participation in school organizations has helped me to become a real team player, knowing where and how to make a group of people maximize their potentials to reach common objectives. I have brought this skill even during my college and early years as a professional, and it is one of my personality traits that I consider useful as I carve my career path. Being my biggest critic, I also had to conquer other grounds as I moved to places. I took an Intensive English course so I could learn to effectively communicate in writing and speech on top of my native language. I know that having the right communications skills will put me ahead of the others, and so I focused on learning not only the language, but more importantly, on achieving the right amount of self confidence to actually communicate and speak in public. This is one of the best decisions I have made because it has enabled me to interact more effectively with people from other cultures, in the workplace and beyond. Most of my career life has been focused on being involved in business analytics, studying performances of partner suppliers and making appropriate recommendations. During my three and a half years of stay with the company Saudi Basic Industries Corporation (SABIC), I was able to enhance my

Assessment Accommodation Research Paper Example | Topics and Well Written Essays - 500 words

Assessment Accommodation - Research Paper Example Accommodation is a word that can be described as an adjustment of the certain environment or a curriculum format to allow an individual to have an access to the learnings that he could gain from it or to somehow to complete the assigned tasks. An example of accommodation is the use of sign language in the teaching-learning process in order for the student to understand the lesson. If accommodation is known to be the â€Å"adjustment† or â€Å"alteration† of the curriculum to accommodate the student’s needs, the modification is the â€Å"change in the curriculum† for the students who cannot go with the actual comprehension process during the class discussion. An example of this is the reduction of the number of assignments for a certain student who has a lower level of comprehension compare to an average student. There are times when teachers commit the mistake of thinking she is in a classroom with the homogenous type of students. However, in reality, students, in general, are heterogeneous. Students have different needs and different weaknesses. Take this status-quo for instance: â€Å"Based on Census and Immigration and Naturalization Services records, it is estimated that there are79 million school-age language minority children in the United States. This bilingual population is distributed throughout the United States with heavier concentrations in the southwest and northeast. The highest concentration is in the large urban areas.† (http://www.teachervision.fen.com) You need to be sure that your student can understand the language or the vocabulary level that is being used in discussing the lesson. If not, it is important to teach them first the essential vocabulary that they need to understand.  Ã‚