Research Topics: Statistics And Its Purpose

Statistics and its purpose

Part A: The use of statistics   Statistics and its purpose   Statistics can be defined as the science of dealing with variability and uncertainty. Almost all measurements made by scientists and people in many other fields are uncertain in some way. In particular, most measurement devices have limited accuracy, so there is uncertainty about the exact value. Sometimes what is being measured varies from individual to individual and from time to time, making it impossible to measure the true average exactly. Statistics has become the approach that the modern world takes to analyzing figures (Kault 2003). Anybody who has to deal with making decisions on the basis of figures who simply looks at the figures rather than get stats done on them, whether they are a researcher or an administrator, would be regarded as inadequate in their job and unable to cope with the intelligent, modern approach. Statistics is a way of making a decision about whether differences are for real or just a result of chance (Kault 2003).     The form of statistics in common use attempts to be entirely objective and so just looks at the figures available and entirely ignores any common sense knowledge of the area.  As a result, statistics cannot directly answer the question is there a real difference? Instead, it answers an indirectly related question: If people were to blame coincidence for the difference, what sort of coincidence would we be talking about. Statistics can help researchers make wiser decisions about situations where there is variability and uncertainty, but there is no method for always making a correct decision (Kault 2003). There are many statistics and many ways to summarize data. Means and correlation coefficients are just examples. However, statistics almost always provide information about just one of two issues. First, some statistics provide summary information on scores obtained on a single variable. Second, statistics provide information about how values on two or more variables vary together. In this role, statistics are used to address the central issue in research which is the relationships between variables. Statistics also serve two purposes. First, they are used to summarize scores and empirical relationships among the cases studied.  Second, statistical procedures are used to address two types of validity (Schwab 2005). One of these involves the contribution of statistics to causal analysis which is the internal statistical validity and validation. The other applies when statistics are used in generalization or statistical generalization validity and validation. Recognizing differences between the levels of measurement is important for the choice of statistics in some instances; it is also important for the interpretation of statistical output (Schwab 2005).   Statistics are used in gathering data; most kind of studies use such field to understand a certain scenario. Its scope has reached wider territories and it has gained advancements that prove valuable to researchers.  The data used in Statistics can be acquired through the use of qualitative and quantitative research. This part of the paper describes the differences between quantitative and qualitative data techniques in research and discusses the situations in which these approaches are more appropriate. Quantitative Analysis Surveys and experiments are probably the main vehicles of quantitative research. The analysis of previously collected data, like official statistics on crime, suicide, unemployment, health, and so on, can be subsumed within the tradition of quantitative research. Quantitative research is a genre which uses a special language which appears to exhibit some similarity to the ways in which scientists talk about how they investigate the natural order of variables, control, measurement, experiment. This superficial imagery reflects the tendency for quantitative research to be under-pinned by a natural science model, which means that the logic and procedures of the natural sciences are taken to provide an epistemological yardstick against which empirical research in the social sciences must be appraised before it can be treated as valid knowledge (Bryman 1992). The epistemology upon which quantitative research is erected comprises a litany of preconditions for what is warrantable knowledge, and the mere presence of numbers is unlikely to be sufficient. Nor is it the emphasis on accumulating quantitative data by those working within the tradition that the critics of quantitative research find unacceptable (Bryman 1992).   Quantitative research is often conceptualized by its practitioners as having a logical structure in which theories determine the problems to which researchers address themselves in the form of hypotheses derived from general theories. These hypotheses are invariably assumed to take the form of expectations about likely causal connections between the concepts which are the constituent elements of the hypotheses. Because concepts in the social sciences are frequently believed to be abstract, there is seen to be a need to provide operational definitions whereby their degrees of variation and co-variation may be measured. Data are collected by questionnaires or other data gathering devices.  Once the survey or experimental data have been collected, they are then analyzed so that the causal connection specified by the hypothesis can be verified or rejected. The resulting findings then feed back into, and are absorbed by, the theory that set the whole process going in the first place (Bryman 1992).Quantitative research exhibits a concern that investigations should be capable of replication. This means that it should be possible for a researcher to employ the same procedures as those used in another study to check on the validity of the initial investigation. Replication can act as a check to establish whether a set of findings can be repeated in another milieu.  In this sense, the issue of replication links closely to the question of generalizability. A second rationale for emphasizing the replicability of research is to ensure that the biases and predilections of researchers can be checked, by allowing their findings to be verified (Bryman 1995).   If the same research design and measurement procedures can be employed by someone else, confidence in the initial findings can be enhanced. Again, the belief in the importance of replication can be traced to the use of the natural sciences as a model of the quantitative research process, since it is generally assumed that it should be possible to verify a scientist’s findings by using the same procedures. One of the reasons for the distrust of qualitative research among some proponents of quantitative research is that the former does not readily permit replication. Quantitative research is claimed to be infused with positivism, an approach to the study of people which commends the application of the scientific method (Creswell 1994).  Qualitative research is often claimed to reflect a different form of knowledge in which people’s understandings of the nature of their social environment form the focus of attention, a focus which contrasts sharply with the tendency in much quantitative research to treat facets of this environment as pre-existing objects akin to the physical or biological matter on which natural scientists work (Bryman 1995).     Quantitative research’s goal is to make use of mathematical data to understand natural phenomena. Quantitative research develops instruments and methods for measurement; create experimental control and manipulation of variables; collect empirical data create Models to analyze data and use such model to evaluate results. In some instances Quantitative research allows the use of proxies as temporary replacements for quantities that cannot be directly measured.  The proxies only reconfigure a certain amount of the variance of the original quantities. Quantitative research methods permit a flexible approach to gathering data.  In this method the choice and design of methods are constantly modified during data gathering based on continuing analysis. This gives way for creation of an investigation of important new issues, concerns, probabilities and questions as they arose. Qualitative Research Qualitative research designs in the social sciences stem from traditions in anthropology and sociology, where the philosophy emphasizes the phenomenological basis of a study, the elaborate description of the meaning of phenomena for the people or culture under examination. Often in a qualitative design only one subject, one case, or one unit is the focus of investigation over an extended period of time. Qualitative research is multi method in focus, involving an interpretive, naturalistic approach to its subject matter. This means that qualitative researchers study things in their natural settings, attempting to make sense of, or interpret, phenomena in terms of the meanings people bring to them. Qualitative research involves the studied use and collection of a variety of empirical material such as case study, personal experience, introspective, life story, interview, observational, historical, interactions, and visual texts on the described routine and problematic moments and meanings in individuals’ lives. Observation is the most frequent data-collection method used in qualitative research. Observation has greater face validity than a second-hand account gathered either through interviewing or document study (Benz & Newman 1998).   Observation is the technique of gathering data through direct contact with usually another human being. The researcher watches the behavior and documents the properties of the object. It is a very important method of data collection used by both qualitative and quantitative researchers. Quantitative scholars usually have an a priori highly structured plan that directs them to remain aloof and observe certain behaviors. In contrast, qualitative researchers usually observe from a phenomenological perspective; they immerse themselves in natural environments and watch a situation as a diffuse, ambiguous entity and allow themselves to be struck with certain peculiarities or interesting happenings. In many examples of qualitative research, the researcher goes into the field to observe and interview people. This raises an important concern about how the researcher is to present him or herself in the community being studied. One option is that researchers could be anonymous so no one in the situation being studied would know the researcher is there to gather data. The interpretive nature of qualitative research does indeed present a real problem to scholars who attempt to explain the process. This is why most theoreticians do not explicate the process of analysis as a set of steps. Rather, they talk about the analysis process as an organic whole that begins in the data-gathering stage and does not end until the writing is completed. The process allows for multiple iterative passes back and forth from data gathering to writing and back to data gathering (Potter 1996).   Reliability refers to consistency in measurement. In common terms the reliability of a test is the extent to which subsequent administrations would give similar results. A test which is not reliable will give different results every time it is taken. Accepted practice uses such measures as test-retest reliability coefficients to indicate reliability. In qualitative research, reliability suggests that different qualitative researchers would come to the same conclusions given exposure to the same situations. The extent to which data relate to objective criteria will improve reliability. When the data are based on personal impressions they tend not to be reliable. However, when they relate to counts or physical measurements or the number of correct math problems, they are generally reliable (Anderson 1998). There are two basic approaches to defining qualitative research problems, open and focused. An inquiry with an open problem is used when little is known about the subject under consideration. It entails collecting a broad spectrum of data and is typically used to discover the nature of the phenomenon, often leading to hypotheses as well as conclusions. Qualitative and quantitative researchers alike define problems, select research designs, develop methodologies, collect, analyze and interpret data, and report findings. There is, however, one significant difference between the two. In qualitative research, the researcher is the principal data collection instrument; whereas in quantitative research, scientifically designed data collection tools are developed (Anderson 1998). Qualitative research intends to find theories that would explain the relationship of one variable with another variable through qualitative elements or components in research. These qualitative elements do not have standard measures; rather, they are behavior, attitudes, opinions, and beliefs. The qualitative research is described as multi-method in focus, involving an interpretative, naturalistic approach to its subject matter. This means that a qualitative researching procedure acts on studying things in their natural settings, attempting to make sense of situations, or interpret events in terms of the meanings people bring to them. References for Part A Anderson, G 1998, Fundamentals of educational research, Falmer, London.   Benz, CR & Newman, I 1998, Qualitative-Quantitative research methodology: Exploring the interactive continuum, Southern Illinois University Press, Carbondale,   Bryman, A 1995, Research methods and organization studies, Routledge, London.   Bryman, A 1992, Quantity and Quality in social research, Routledge, London.   Creswell, JW 1994, Research design: qualitative and quantitative approaches, Sage, Thousand Oaks, California.   Kault, D 2003, Statistics with common sense, Greenwood Press, Westport, CT.   Potter, WJ 1996, An analysis of thinking and research about Qualitative methods, Lawrence Erlbaum Associates, Mahwah, NJ.   Schwab, DP 2005, Research methods for organizational studies, Lawrence Erlbaum Associates, Mahwah, NJ.                                           Part B Research on a company Apple Computers Inc Apple was founded by Steven Jobs and Stephen Wozniak in 1976; Apple Computer Company revolutionized the personal computer industry and epitomized the rise of clean industry in the New West. Located in the Santa Clara Valley, in California, the company’s first product was the Apple I, a single-board computer with on-board read-only memory (ROM), which sold for about 0 without a monitor or keyboard. Orders instantly soared, and Jobs and Wozniak quickly brought out the Apple II, which included a keyboard, color monitor, and expansions for peripheral devices (Birzer & Schweikart 2003). In 1984, Apple introduced the Macintosh, which was aimed at the business and education markets, by which time the company had already not only changed American industry but had reshaped entire areas of the West around silicon. In 1996, after a series of CEOs failed to keep Apple profitable, Steve Jobs returned under the rubric interim CEO and soon launched a new marketing and licensing relationship with Microsoft. In 2000 his direct sales concept, the Apple Store brought the company back to profitability (Birzer & Schweikart 2003).In 1994 Apple computers launched a new line of computers based on the PowerPC processor chip. The creation of the new chip was a joint venture between Apple Computers, IBM, and Motorola, and because the new chip was capable of being compatible with the market leading Intel chip, it was marketed as a major breakthrough in computer technology. If emulation software was purchased by a consumer, the consumer could run both software made for Apple computers and software made for Intel PCs on the same Apple machine. The machine was even being called a PC with a free Mac inside. Apple computers had controlled about 8-10 percent of the personal computer market since 1984, and recently it had been struggling financially (Gottinger 2003).  Those at Apple hoped that compatibility with the Intel-based PC and its 85 per cent market share would dramatically increase the market share of Apple computers. The results from the introduction of the new product were not everything Apple had predicted or had hoped for. The increased competition from the PowerPC chip forced Intel to slash the price of their Pentium chips by 40 per cent. Thus Apple did not live up to its promise of cheaper computers (Gottinger 2003).    Early in 1996 the Apple computer company ran into deep trouble. It managed to lose seven hundred million dollars in a single quarter, which is more than most businesses earn their whole lives. The company’s very survival was in danger, and economists, businessmen, and technology pundits were at a loss. Apple computers were beautiful in the classic technology sense, simple and powerful. They were attractive in an important area particularly the machine’s operating system (Gelernter 1997). Apple Computers Inc is considered to be one of the innovators in the computer industry. It brought about different changes to the industry; these changes are still visible in the present.  The company’s products were used as a basis by other computer company’s in designing the specifications and physical characteristics of their product. It also serves as a meter of how products are designed. Apple Computers Inc. has made products for its consumers found in various parts of the world. Website Apple Inc. makes use of various technological innovations that help in increasing productivity and improving the quality of their products. The technologies that used by the company passed international standards and its benefits were proven by various companies. The company makes further use of technology by using it as a means for the organization to provide easier way for the clients to transact business with them. Technology such as the company’s website was used by the company as an alternative means for them to do business with their clients. The website of Apple is designed in an attractive way wherein its various products have been arranged accordingly. When one clicks a certain label for a product, the company’s product line emerges and various information and specification for a product appears.  The website has an online purchase function wherein one who wants to purchase his/her desired product can choose his/her preferred specification for the product, his/her payment procedures and other important information that the company needs to have.   Products/Services Apple sells Computers, Computer Softwares, Ipod/MP3 player and Iphone/Cellular phone. The company’s products were used as a basis by other computer company’s in designing the specifications and physical characteristics of their product. It also serves as a meter of how products are designed.  For instance the company’s I-pod mp3 player is one of the most popular mp3 players available in the market.  It has evolved from a simple mp3 player into a portable device wherein the user can watch movies or videos through it. Apple Computers Inc and its product showed that with the use of proper strategy and use of its varied opportunities the company can achieve fast growth and development in a short period of time. The company provides support service for its entire product. In the company’s website, downloads and other support systems are available for clients who have purchased their product. The company’s website has a section where helpful information about the products can be found. This section contains what the client can do once a product is not functioning properly. The section also contains additional instructions on how the product can be used well.  Within this section are the specifications and capacities of the product.  The website also features a section where clients can contact designated personnel of the company to address certain issues with the product and other kinds of inquiries.    The company has installed different service centers on different places in the world; they can assist anybody who has problems with their products.  The company has also allowed resellers to provide repairs on products they may find defective. Moreover the company offers self repair courses for companies or individuals who want to learn about fixing their products that have some issues. The market of Apple Inc is students and professionals who need computers and other digital technologies. This market is the one that needs devices that can keep their records and other personal or business information. This market is the one that needs devices that can give them entertainment even if they are not in their own homes. This market is the one that would want devices that would not cause them to waste their time.  The marketing orientation that the company tries to implement is deeper customer focus. This type of orientation provides assistance for the company to achieve their goals and provide effective service compared to competitors.     Growth The globalization of markets, manufacturing and techno-industrial innovation therefore gives particular importance to the different kinds of networking. In contrast to previous forms of the international division of lab our, location participation is less denned by contributing products than by contributing to the various processes of production. These highly globalize processes are decisive for both different types and different opportunities for industrial development that can be identified at different industrial locations (Hilpert 2003). Global tendencies in industrial development are leading to a more complex form of the international division of labor. While the relocation of mature and old industries has induced regional crisis in the traditional industrial centers, now the transfer of such industrial capabilities provides the basis for advanced industries to keep costs under control and to gain competitiveness based on low production costs at locations where suppliers for these parts are based. This kind of hierarchical integration is based on different production costs and demands successful networking between locations that are on different levels of industrial development. Depending upon the competitive situation and the opportunities to gain benefits from relocating manufacturing, there is a tendency towards the integration of new industrial locations (Hilpert 2003). The pre-existing regional structure, the very specific requirements for these new technologies and new forms of industrial development, and the need for immediate realization of these processes consequently do not take into regard attempts at regional development (Hilpert 2003).    Developments in certain industrial sectors have a regional expression, and these regions also form the basis for uneven economic development. Whilst not denying the importance of public policies, regional development to a great extent follows from the geographical expression of national industrial capabilities. Even though many of the previous centers of industrial development reemerge in relation to current innovations, the regionalized division of labor changes with regard to new technologies (Hilpert 2003). Industrial development had its attention on the making sure that the country will have a better standing in its environment. Apple has grown over the years, its product range has widened and its market segment has expanded. From a single computer, the company has now sold millions of computers and other devices that their clients need.  The company is known by most people due to their product lines, unwavering service, captivating logo and brand name. The company has branches, partners and service centers in around 30 countries and it continues to expand to more territories. The products of apple helped in spreading the concept of globalization to various parts of the world.   Performance compared with competitors Compared with the competitors such as Microsoft and Dell, the company is doing fairly well and it tries to gain financial numbers that does not stray far from its competitors. Apple computers use Derivatives to undertaken to manage existing risks facing the company. The use of derivatives helps the company to gain a better financial standing for the company. For Apple computers, it places bets on the volatility of underlying security to speculate on traded options.  The company also engages in exchange traded derivatives where the company exchanges products over specialized derivatives exchanges.   Finances   2007 2006 2005 Revenue ($ mil.) 24,006.0 19,315.0 13,931.0 Gross Profit ($ mil.) 8,154.0 5,598.0 4,043.0 Operating Income ($ mil.) 4,409.0 2,453.0 1,650.0 Total Net Income ($ mil.) 3,496.0 1,989.0 1,335.0 Diluted EPS (Net Income) 3.93 2.27 1.56 (From www.hoovers.com) Based from the company’s financial statement, the company has increased its Revenue, Gross Profit, Operating Income, Total net income and Diluted Earnings per Share. In terms of yearly data, the company is financially successful and the financial strategies that it currently uses are working well.  Although there is a decrease in gross profit in 2006, overall the company has maintained its financial standing and market value over the years. If this trend continues they may soon gain advantage over their rivals. Management/staff Apple is run well by competent and reliable managers and personnel. Each member of the management team has individual credentials that no other company can match.  Each member of the management has been trained to make the best decision for the firm. Currently the company has around 28,000. These employees have been chosen well by the HR department and they have qualities that best fits the company.   Operations Apple is run and managed by the most capable people. The management team makes sure that the company’s day to day operations will run smoothly. The management team is immediately informed of any problems between suppliers, plants or any other issues.  The procedures and processes used in creating the product and giving services have been strategically devised.   Customer Services As previously mentioned the company has installed different service centers on different places in the world; they can assist anybody who has problems with their products.  The company has also allowed resellers to provide repairs on products they may find defective. Moreover the company offers self repair courses for companies or individuals who want to learn about fixing their products that have some issues. The company and its subsidiaries can be contacted through the phone, email or through the website itself. References for part B Apple Inc 2008, Company Profile, viewed 15 August, 2008, <http://www.apple.com/>.   Gelernter, D 1997, Machine beauty: elegance and the heart of technology, Basic Books, New York.   Gottinger, HW 2003, Economies of network industries, Routledge, New York. Hilpert, U (ed.) 2003, Regionalization of globalized innovation: locations for advanced industrial development and disparities in participation, Routledge, New York.   Hoovers Online 1994, Apple key numbers, viewed 15 August, 2008, <http://www.hoovers.com>.   Mckern, B 2003, Managing the global network corporation, Routledge, London.   Robson, P 1998, The economics of international integration, Routledge, London.   Toporowski, J 2000, The end of finance: the theory of capital market inflation, financial derivatives, and Pension Fund Capitalism, Routledge, London.            Credit:ivythesis.typepad.com

Statistics and its purpose

Part A: The use of statistics Statistics and its purpose Statistics can be defined as the science of dealing with variability and un...

STATISTICS FOR MANAGER

MBA in Management  Statistics for Managers Final Exam Paper 1.                   Samples of light bulbs were obtained from two suppliers and tested ‘to destruction’ in the laboratory. The following results were obtained for the length of life:   Length of Life (hours)   700-899 900-1099 1100-1299 1300-1499 Total Supplier A 14 16 26 12 68 Supplier B 5 36 21 5 67   (a)   Which supplier’s bulbs have greater average length of life? For easier computation, the class intervals were assigned numbers. Interval 700-899 is 1; 900-1099 is 2; 1100-1299 is 3; and 1300-1499 is 4. SUPPLIER A      = 14 (1) + 16 (2) + 26 (3) + 12 (4) / 68                                           = 2.53 or 3 l 3 or class interval 1100-1299 is the average length of life for Supplier A. SUPPLIER B      = 5 (1) + 36 (2) + 21 (3) + 5 (4) / 67                                           = 2.39 or 2 l 2 or class interval 900-1099 is the average length of life for Supplier B. ll Supplier A has bulbs that have a greater average length of life, from 1100 to 1299 hours, compared to Supplier B, whose bulbs have an average length of life is from 900-1099 hours only. (b)   Which supplier’s bulbs are more uniform in quality? Supplier A mean = 17                                             Supplier A standard deviation = 5.38 Supplier B mean = 16.75                           Supplier B Standard deviation = 12.89                                                   5.38                                                    17                                     =          .3165 or 31.7%                                                     12.89                                                   16.75                                     =          .77 or 77%   l The bulbs of Supplier A are more uniform in quality, as a lower coefficient of variation denotes that the bulbs are more uniform in quality. (c)   Which supplier would you prefer to use? I would prefer to use Supplier A based on the above computations, because their light bulbs proved to be more cost-efficient, as the bulbs have a greater average length of life and are more uniform in quality than those of Supplier B. 2.                   At the end of an MBA course in business statistics, the final examination grades have a mean of 70.2 and a standard deviation of 12.3. There were 210 students on the course. Assuming that the distribution of these grades (all whole numbers) in normal, find: (a)   the percentage of grades that should exceed 90 Z    = 90 – 70.2                               12.3                   = 1.61 P (to the right of Z = 1.61)       = .5 – .4463       = .054 or 5.4% l There is a 5.4% percentage of grades that should exceed 90. (b)   the percentage of grades less than 35 Z    = 35 – 70.2                               12.3                   = -2.86 P (to the left of Z = -2.86)       = .5 – .4979       = .0021 or .21% l There is a .21% percentage of grades less than 35. (c)   the number of failures (pass = 70 per cent)     69.9 – 70.2         12.3               Z        = .024                P (to the right of Z = .024)   P           = .5 – .0080     = .492 or 49.2%     49.2 % x 210 = 103.32 or 104 l There are 104 students out of 210 students who failed the final examination. (d)               the lowest distinction mark if at most the highest 5 per cent of grades are to be awarded distinctions. Z = .45 = 1.645   x – 70.2    12.3   x = (12.3) (1.645) + 70.2  = 90.43   l The lowest distinction mark in the highest 5 percent of grades is 90.43. 3.                  , researcher for the Colombian Coffee Corporation is interested in determining the rate of coffee usage per household in the United Sates. She believes that yearly consumption per household is normally distributed with an unknown mean and a standard deviation of about 2 pounds. a)                 If  takes a sample of 16 households and records their consumption of coffee for one year, what is the probability that the sample mean is within one pound of the population mean? Z       = .1915 x 2                      = .383 or 38.3% l The probability that the sample mean is within one pound of the population mean is 38.3%. b)                  How large a sample must she take in order to be 98 percent certain that the sample mean is within one pound of the population mean?     38.3                                98   16                                    n                 n = 40.94 or 41 l Ms.  must take 41 samples in order to be 98 percent certain that the sample mean is within one pound of the population mean. 4.                  A chain of department stores is moving into a phase of expansion and opening several new stores. As part of the expansion planning process a project team is carrying out an investigation to find out how the sales levels at new stores might be predicted. One approach has been to use regression analysis. The average level of sales per week (y) for each existing store in the chain (fourteen department stores) together with a measure of disposable income per family in each store’s catchment area are given in Table 11.1 Table 11.1 Store number Average sales per week (₤000s) Y Average disposable family income (coded) x 1 90 301 2 97 267 3 86 397 4 84 227 5 82 273 6 80 253 7 78 203 8 75 263 9 70 190 10 68 212 11 64 157 12 61 141 13 58 119 14 52 133 Mean 74 217 The computer gives the following results after regressing sales against family income: Variable                     Coefficient Income                       0.17846 Constant        35.228 Correlations Coefficient = 0.92 Standard error = 4.72   (a)               According to the above table, what is the predictable average sales per week with average family disposable income at 221? y = a + bx     = 35.228 + .17846 (221) y  = 74.67 l The predictable average sale per week assuming disposable income is at 221 is 74.67. (b)        How good is the application of regression analysis in the above data? The correlations coefficient and the standard error results are suffice evidence that the application of regression analysis in the above data is reliable. The data from the average sales per week is the endogenous and dependent variable in the regression analysis, while the average disposable family income is the exogenous or the independent variable, changes on it that the former reacts to. Correlation coefficient values ranges from negative one to positive one, and a value closer to one (either negative or positive) indicates higher relationship between the two variables. Two closely related variables used in a regression analysis produce more accurate results in showing how changes in the independent variable affects the dependent variable, which, in this case, is the sales per week. (c)        What are the limitations of this method to predict the average sales per week? For one, there are other factors affecting the computation of sales other than the disposable family income of the consumers. These other factors may come in the form of inflation and interest rates, equity markets, amount of advertising expenditures and number of competitors, which the use of a multiple linear regression would sufficiently accommodate. The other limitation is that the values that can be accurately predicted are restricted to a certain range. Thus, computations for values outside the range will be doubtful because the investigation provided no evidence as to the nature of the statistical relationship outside the existing range. 5.                  Factory A conducted a sample check of total number of apples per crate and get the following results. The Quality Manager would like to see if the data are out of control. Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 110 93 99 98 109 103 95 109 95 98 97 110 90 97 100 96 102 105 90 96 105 110 109 93 98 110 91 104 91 101 100 96 104 93 96 93 90 110 109 105 90 105 109 90 108 103 93 93 99 96 97 97 104 103 92 103 100 91 103 105 90 101 96 104 108 97 106 97 105 96 99 94 96 98 90 106 93 104 93 99 90 95 98 109 110 96 96 108 97 103 109 96 91 98 109 90 95 94 107 99 91 101 96 96 109 108 97 101 103 94 96 97 106 96 98 101 107 104 109 104 96 91 96 91 105 (a)       Calculate LCL & UCL UCLx   = x + A2 R                                                                  UCLR  = D4 R = 99.54 + (.58) 19.8                                                                      = 2.11 (19.8) UCLx   = 111.02                                                                     UCLR = 41.78   LCLx   = x – A2 R                                                                   LCLR   = D3 R                         = 99.54 – (.58) 19.8                                                               = 0 (19.8) LCLx   = 88.06                                                                                   LCLR   = 0   (b)       Calculate Average of Mean ( x ) Sample1x= 99       Sample2x= 98           Sample3x= 101 Sample4x= 98.7            Sample5x= 101             x          = 99 + 98 + 101 + 98.7 + 101             x          = 99.54 (c)        Draw the X – R chart Credit:ivythesis.typepad.com

STATISTICS FOR MANAGER

MBA in Management Statistics for Managers Final Exam Paper 1. Samples of light bulbs were obtained from two su...