Ebook Business statistics (7th edition): Part 2

(BQ) Part 2 book Business statistics has contents: Simple linear regression and correlation, multiple regression, time series, forecasting, and index numbers, quality control and improvement, bayesian statistics and decision analysis, sampling methods, multivariate analysis,...and other contents.

410 1 1 www.downloadslide.com Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition 10 Simple Linear Regression and Correlation 10 Text © The McGraw−Hill Companies, 2009 SIMPLE LINEAR REGRESSION AND CORRELATION 10–1 10–2 10–3 10–4 1 1 Using Statistics 409 The Simple Linear Regression Model 411 Estimation: The Method of Least Squares 414 Error Variance and the Standard Errors of Regression Estimators 424 10–5 Correlation 429 10–6 Hypothesis Tests about the Regression Relationship 434 10–7 How Good Is the Regression? 438 10–8 Analysis-of-Variance Table and an F Test of the Regression Model 443 10–9 Residual Analysis and Checking for Model Inadequacies 445 10–10 Use of the Regression Model for Prediction 454 10–11 Using the Computer 458 10–12 Summary and Review of Terms 464 Case 13 Firm Leverage and Shareholder Rights 466 Case 14 Risk and Return 467 LEARNING OBJECTIVES 408 After studying this chapter, you should be able to: • Determine whether a regression experiment would be useful in a given instance • Formulate a regression model • Compute a regression equation • Compute the covariance and the correlation coefficient of two random variables • Compute confidence intervals for regression coefficients • Compute a prediction interval for a dependent variable • Test hypotheses about regression coefficients • Conduct an ANOVA experiment using regression results • Analyze residuals to check the validity of assumptions about the regression model • Solve regression problems using spreadsheet templates • Use the LINEST function to carry out a regression 1 1 www.downloadslide.com Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition 10 Simple Linear Regression and Correlation Text 10–1 Using Statistics In 1855, a 33-year-old Englishman settled down to a life of leisure in London after several years of travel throughout Europe and Africa The boredom brought about by a comfortable life induced him to write, and his first book was, naturally, The Art of Travel As his intellectual curiosity grew, he shifted his interests to science and many years later published a paper on heredity, “Natural Inheritance” (1889) He reported his discovery that sizes of seeds of sweet pea plants appeared to “revert,” or “regress,” to the mean size in successive generations He also reported results of a study of the relationship between heights of fathers and the heights of their sons A straight line was fit to the data pairs: height of son versus height of father Here, too, he found a “regression to mediocrity”: The heights of the sons represented a movement away from their fathers, toward the average height The man was Sir Francis Galton, a cousin of Charles Darwin We credit him with the idea of statistical regression While most applications of regression analysis may have little to with the “regression to the mean” discovered by Galton, the term regression remains It now refers to the statistical technique of modeling the relationship between variables In this chapter on simple linear regression, we model the relationship between two variables: a dependent variable, denoted by Y, and an independent variable, denoted by X The model we use is a straight-line relationship between X and Y When we model the relationship between the dependent variableY and a set of several independent variables, or when the assumed relationship between Y and X is curved and requires the use of more terms in the model, we use a technique called multiple regression This technique will be discussed in the next chapter Figure 10–1 is a general example of simple linear regression: fitting a straight line to describe the relationship between two variables X and Y The points on the graph are randomly chosen observations of the two variables X andY, and the straight line describes the general movement in the data—an increase in Y corresponding to an increase in X An inverse straight-line relationship is also possible, consisting of a general decrease in Y as X increases (in such cases, the slope of the line is negative) Regression analysis is one of the most important and widely used statistical techniques and has many applications in business and economics A firm may be interested in estimating the relationship between advertising and sales (one of the most important topics of research in the field of marketing) Over a short range of values— when advertising is not yet overdone, giving diminishing returns—the relationship between advertising and sales may be well approximated by a straight line The X variable in Figure 10–1 could denote advertising expenditure, and the Y variable could stand for the resulting sales for the same period The data points in this case would be pairs of observations of the form x1 ϭ $75,570, y1 ϭ 134,679 units; x ϭ $83,090, y2 ϭ 151,664 units; etc That is, the first month the firm spent $75,570 on advertising, and sales for the month were 134,679 units; the second month the company spent $83,090 on advertising, with resulting sales of 151,664 units for that month; and so on for the entire set of available data The data pairs, values of X paired with corresponding values of Y, are the points shown in a sketch of the data (such as Figure 10–1) A sketch of data on two variables is called a scatter plot In addition to the scatter plot, Figure 10–1 shows the straight line believed to best show how the general trend of increasing sales corresponds, in this example, to increasing advertising expenditures This chapter will teach you how to find the best line to fit a data set and how to use the line once you have found it © The McGraw−Hill Companies, 2009 411 1 1 www.downloadslide.com 412 Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition 410 10 Simple Linear Regression and Correlation © The McGraw−Hill Companies, 2009 Text Chapter 10 FIGURE 10–1 Simple Linear Regression y Data point Regression line x Although, in reality, our sample may consist of all available information on the two variables under study, we always assume that our data set constitutes a random sample of observations from a population of possible pairs of values of X and Y Incidentally, in our hypothetical advertising sales example, we assume no carryover effect of advertising from month to month; every month’s sales depend only on that month’s level of advertising Other common examples of the use of simple linear regression in business and economics are the modeling of the relationship between job performance (the dependent variable Y ) and extent of training (the independent variable X ); the relationship between returns on a stock (Y ) and the riskiness of the stock (X ); and the relationship between company profits (Y ) and the state of the economy (X ) Model Building FIGURE 10–2 A Statistical Model Data Statistical model Systematic component ϩ Random errors Model extracts everything systematic in the data, leaving purely random errors Like the analysis of variance, both simple linear regression and multiple regression are statistical models Recall that a statistical model is a set of mathematical formulas and assumptions that describe a real-world situation We would like our model to explain as much as possible about the process underlying our data However, due to the uncertainty inherent in all real-world situations, our model will probably not explain everything, and we will always have some remaining errors The errors are due to unknown outside factors that affect the process generating our data A good statistical model is parsimonious, which means that it uses as few mathematical terms as possible to describe the real situation The model captures the systematic behavior of the data, leaving out the factors that are nonsystematic and cannot be foreseen or predicted—the errors The idea of a good statistical model is illustrated in Figure 10–2 The errors, denoted by ⑀, constitute the random component in the model In a sense, the statistical model breaks down the data into a nonrandom, systematic component, which can be described by a formula, and a purely random component How we deal with the errors? This is where probability theory comes in Since our model, we hope, captures everything systematic in the data, the remaining random errors are probably due to a large number of minor factors that we cannot trace We assume that the random errors ⑀ are normally distributed If we have a properly constructed model, the resulting observed errors will have an average of zero (although few, if any, will actually equal zero), and they should also be independent of one another We note that the assumption of a normal distribution of the errors is not absolutely necessary in the regression model The assumption is made so that we can carry out statistical hypothesis tests using the F and t distributions The only necessary assumption is that the errors ⑀ have mean zero and a constant variance ␴2 and that they be uncorrelated with one another In the www.downloadslide.com Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition 10 Simple Linear Regression and Correlation Simple Linear Regression and Correlation FIGURE 10–3 411 Steps in Building a Statistical Model Specify a statistical model: formula and assumptions Estimate the parameters of the model from the data set Examine the residuals and test for appropriateness of the model 413 © The McGraw−Hill Companies, 2009 Text If the model is not appropriate Use the model for its intended purpose next section, we describe the simple linear regression model We now present a general model-building methodology First, we propose a particular model to describe a given situation For example, we may propose a simple linear regression model for describing the relationship between two variables Then we estimate the model parameters from the random sample of data we have The next step is to consider the observed errors resulting from the fit of the model to the data These observed errors, called residuals, represent the information in the data not explained by the model For example, in the ANOVA model discussed in Chapter 9, the within-group variation (leading to SSE and MSE) is due to the residuals If the residuals are found to contain some nonrandom, systematic component, we reevaluate our proposed model and, if possible, adjust it to incorporate the systematic component found in the residuals; or we may have to discard the model and try another When we believe that model residuals contain nothing more than pure randomness, we use the model for its intended purpose: prediction of a variable, control of a variable, or the explanation of the relationships among variables In the advertising sales example, once the regression model has been estimated and found to be appropriate, the firm may be able to use the model for predicting sales for a given level of advertising within the range of values studied Using the model, the firm may be able to control its sales by setting the level of advertising expenditure The model may help explain the effect of advertising on sales within the range of values studied Figure 10–3 shows the usual steps of building a statistical model 10–2 The Simple Linear Regression Model Recall from algebra that the equation of a straight line is Y ϭ A ϩ BX, where A is the Y intercept and B is the slope of the line In simple linear regression, we model the relationship between two variables X and Y as a straight line Therefore, our model must contain two parameters: an intercept parameter and a slope parameter The usual notation for the population intercept is ␤0, and the notation for the population slope is ␤1 If we include the error term ⑀, the population regression model is given in equation 10–1 V F S CHAPTER 15 www.downloadslide.com 414 Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition 412 10 Simple Linear Regression and Correlation © The McGraw−Hill Companies, 2009 Text Chapter 10 The population simple linear regression model is Y ϭ ␤0 ϩ ␤1X ϩ ⑀ (10–1) where Y is the dependent variable, the variable we wish to explain or predict; X is the independent variable, also called the predictor variable; and ⑀ is the error term, the only random component in the model and thus the only source of randomness in Y The model parameters are as follows: FIGURE 10–4 Simple Linear Regression Model Y ϭ ␤0 ϩ ␤1X ϩ ⑀ 123 123 Nonrandom component: straight line Random error ␤0 is the Y intercept of the straight line given by Y ϭ ␤0 ϩ ␤1X (the line does not contain the error term) ␤1 is the slope of the line Y ϭ ␤0 ϩ ␤1X The simple linear regression model of equation 10–1 is composed of two components: a nonrandom component, which is the line itself, and a purely random component—the error term ⑀ This is shown in Figure 10–4 The nonrandom part of the model, the straight line, is the equation for the mean of Y, given X We denote the conditional mean of Y, given X, by E(Y | X ) Thus, if the model is correct, the average value of Y for a given value of X falls right on the regression line The equation for the mean of Y, given X, is given as equation 10–2 The conditional mean of Y is E (Y | X) ϭ ␤0 ϩ ␤1X (10–2) Comparing equations 10–1 and 10–2, we see that our model says that each value of Y comprises the average Y for the given value of X (this is the straight line), plus a random error We will sometimes use the simplified notation E (Y ) for the line, remembering that this is the conditional mean of Y for a given value of X As X increases, the average population value of Y also increases, assuming a positive slope of the line (or decreases, if the slope is negative) The actual population value of Y is equal to the average Y conditional on X, plus a random error ⑀ We thus have, for a given value of X, Y ϭ Average Y for given X ϩ Error Figure 10–5 shows the population regression model We now state the assumptions of the simple linear regression model Model assumptions: The relationship between X and Y is a straight-line relationship The values of the independent variable X are assumed fixed (not random); the only randomness in the values of Y comes from the error term ⑀ www.downloadslide.com Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition 10 Simple Linear Regression and Correlation 415 © The McGraw−Hill Companies, 2009 Text Simple Linear Regression and Correlation FIGURE 10–5 413 Population Regression Line y The error ⑀ associated with the point A The points are the population values of X and Y A The regression line E(Y) = β0 + β1X β1 The slope β0 The intercept x The errors ⑀ are normally distributed with mean and a constant variance ␴2 The errors are uncorrelated (not related) with one s: another in successive observations.1 In symbols: ⑀ ϳ N(0, ␴2) FIGURE 10–6 Distributional Assumptions of the Linear Regression Model (10–3) Figure 10–6 shows the distributional assumptions of the errors of the simple linear regression model The population regression errors are normally distributed about the population regression line, with mean zero and equal variance (The errors are equally spread about the regression line; the error variance does not increase or decrease as X increases.) The simple linear regression model applies only if the true relationship between the two variables X and Y is a straight-line relationship If the relationship is curved (curvilinear), then we need to use the more involved methods of the next chapter In Figure 10–7, we show various relationships between two variables Some are straightline relationships that can be modeled by simple linear regression, and others are not So far, we have described the population model, that is, the assumed true relationship between the two variables X and Y Our interest is focused on this unknown population relationship, and we want to estimate it, using sample information We obtain a random sample of observations on the two variables, and we estimate the regression model parameters ␤0 and ␤1 from this sample This is done by the method of least squares, which is discussed in the next section Normal distribution y of the regression errors has mean zero and constant variance (the distributions are centered on the line with equal spread) ␴ ␴ ␴ ␴ x PROBLEMS 10–1 What is a statistical model? 10–2 What are the steps of statistical model building? 10–3 What are the assumptions of the simple linear regression model? 10–4 Define the parameters of the simple linear regression model The idea of statistical correlation will be discussed in detail in Section 10–5 In the case of the regression errors, we assume that successive errors ⑀1, ⑀2, ⑀3, are uncorrelated: they are not related with one another; there is no trend, no joint movement in successive errors Incidentally, the assumption of zero correlation together with the assumption of a normal distribution of the errors implies the assumption that the errors are independent of one another Independence implies noncorrelation, but noncorrelation does not imply independence, except in the case of a normal distribution (this is a technical point) www.downloadslide.com 416 Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition 414 10 Simple Linear Regression and Correlation © The McGraw−Hill Companies, 2009 Text Chapter 10 FIGURE 10–7 Some Possible Relationships between X and Y y y Here a curve describes the relationship better than a line Here a straight line describes the relationship well x x y y Here a straight line describes the relationship well Here a curve, rather than a straight line, is a good description of the relationship x x 10–5 What is the conditional mean of Y, given X ? 10–6 What are the uses of a regression model? 10–7 What are the purpose and meaning of the error term in regression? 10–8 A simple linear regression model was used for predicting the success of private-label products, which, according to the authors of the study, now account for 20% of global grocery sales, and the per capita gross domestic product for the country at which the private-label product is sold.2 The regression equation is given as PLS ϭ ␤ GDPC ϩ ⑀ where PLS ϭ private label success, GDPC ϭ per capita gross domestic product, ␤ ϭ regression slope, and ⑀ ϭ error term What kind of regression model is this? F V S CHAPTER 15 10–3 Estimation: The Method of Least Squares We want to find good estimates of the regression parameters ␤0 and ␤1 Remember the properties of good estimators, discussed in Chapter Unbiasedness and efficiency are among these properties A method that will give us good estimates of the regression Lien Lamey et al., “How Business Cycles Contribute to Private-Label Success: Evidence from the United States and Europe,” Journal of Marketing 71 ( January 2007), pp 1–15 www.downloadslide.com Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition 10 Simple Linear Regression and Correlation Simple Linear Regression and Correlation coefficients is the method of least squares The method of least squares gives us the best linear unbiased estimators (BLUE) of the regression parameters ␤0 and ␤1 These estimators both are unbiased and have the lowest variance of all possible unbiased estimators of the regression parameters These properties of the least-squares estimators are specified by a well-known theorem, the Gauss-Markov theorem We denote the least-squares estimators by b0 and b1 The least-squares estimators are b0 estimates ⎯⎯⎯→ ␤0 b1 estimates ⎯⎯⎯→ ␤1 The estimated regression equation is Y ϭ b0 ϩ b1X ϩ e (10–4) where b0 estimates ␤0 , b1 estimates ␤1, and e stands for the observed errors—the residuals from fitting the line b0 ϩ b1X to the data set of n points In terms of the data, equation 10–4 can be written with the subscript i to signify each particular data point: yi ϭ b0 ϩ b1xi ϩ ei 417 © The McGraw−Hill Companies, 2009 Text (10–5) where i = 1, 2, , n Then e1 is the first residual, the distance from the first data point to the fitted regression line; e is the distance from the second data point to the line; and so on to en , the nth error The errors ei are viewed as estimates of the true population errors ⑀i The equation of the regression line itself is as follows: The regression line is Yˆ ϭ b0 ϩ b1X (10–6) ˆ where Y (pronounced “Y hat”) is the Y value lying on the fitted regression line for a given X Thus, yˆ1 is the fitted value corresponding to x1, that is, the value of y1 without the error e1, and so on for all i ϭ 1, 2, , n The fitted value Y is also called the predicted value of Yˆ because if we not know the actual value of Y, it is the value we would predict for a given value of X, using the estimated regression line Having defined the estimated regression equation, the errors, and the fitted values of Y, we will now demonstrate the principle of least squares, which gives us the BLUE regression parameters Consider the data set shown in Figure 10–8(a) In parts (b ), (c), and (d ) of the figure, we show different lines passing through the data set and the resulting errors ei As can be seen from Figure 10–8, the regression line proposed in part (b ) results in very large errors The errors corresponding to the line of part (c ) are smaller than the ones of part (b), but the errors resulting from using the line proposed in part (d ) are by far the smallest The line in part (d ) seems to move with the data and minimize the resulting errors This should convince you that the line that best describes the trend in the data is the line that lies “inside” the set of 415 www.downloadslide.com 418 Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition 416 10 Simple Linear Regression and Correlation © The McGraw−Hill Companies, 2009 Text Chapter 10 FIGURE 10–8 A Data Set of X and Y Pairs, and Different Proposed Straight Lines to Describe the Data y y (a) (c) Another proposed regression line The data Examples of three of the resulting errors x y x y (b) (d) A proposed regression line The least-squares regression line These are three of the resulting errors, ei The resulting errors are minimized x x points; since some of the points lie above the fitted line and others below the line, some errors will be positive and others will be negative If we want to minimize all the errors (both positive and negative ones), we should minimize the sum of the squared errors (SSE, as in ANOVA) Thus, we want to find the least-squares line—the line that minimizes SSE We note that least squares is not the only method of fitting lines to data; other methods include minimizing the sum of the absolute errors The method of least squares, however, is the most commonly used method to estimate a regression relationship Figure 10–9 shows how the errors lead to the calculation of SSE We define the sum of squares for error in regression as n n i =1 i =1 SSE = a ei2 = a (yi - y$i)2 (10–7) Figure 10–10 shows different values of SSE corresponding to values of b and b1 The least-squares line is the particular line specified by values of b and b1 that minimize SSE, as shown in the figure www.downloadslide.com Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition 10 Simple Linear Regression and Correlation Simple Linear Regression and Correlation FIGURE 10–9 Regression Errors Leading to SSE y Data point (Xi , Yi ) Regression line Y^ = b0 + b1 X Error ei Y^ i , the predicted Y for Xi Error ei = Yi – Y^i SSE = ⌺( ei )2 = ⌺(Yi – Y^i )2 (sum over all data) x Xi FIGURE 10–10 The Particular Values b0 and b1 That Minimize SSE SSE b0 At this point SSE is minimized with respect to b0 and b1 Least squares b0 The corresponding values of b0 and b1 are the least-squares estimates b1 Least squares b1 Calculus is used in finding the expressions for b and b1 that minimize SSE These expressions are called the normal equations and are given as equations 10–8.3 This system of two equations with two unknowns is solved to give us the values of b0 and b1 that minimize SSE The results are the least-squares estimators b0 and b1 of the simple linear regression parameters ␤0 and ␤1 The normal equations are n n a yi = nb0 + b1 a xi i=1 n i=1 n n i=1 i=1 a xiyi = b0 a xi + b1 a xi i=1 419 © The McGraw−Hill Companies, 2009 Text (10–8) We leave it as an exercise to the reader with background in calculus to derive the normal equations by taking the partial derivatives of SSE with respect to b0 and b1 and setting them to zero 417 www.downloadslide.com 870 Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition Back Matter 790 © The McGraw−Hill Companies, 2009 Appendix C: Statistical Tables Appendix C TABLE 13 Control Chart Constants For Estimating Sigma For X Chart For X Chart (Standard Given) For R Chart D3 For R Chart (Standard Given) D4 D1 For s Chart (Standard Given) n c4 d2 A2 A3 A 0.7979 0.8862 1.128 1.693 1.880 1.023 2.659 1.954 2.121 1.732 0 3.267 2.575 0 3.686 4.358 D2 0 B3 3.267 2.568 B4 0 B5 2.606 2.276 B6 0.9213 0.9400 0.9515 2.059 2.326 2.534 0.729 0.577 0.483 1.628 1.427 1.287 1.500 1.342 1.225 0 2.282 2.115 2.004 0 4.698 4.918 5.078 0 0.030 2.266 2.089 1.970 0 0.029 2.088 1.964 1.874 10 15 20 0.9594 0.9650 0.9693 0.9727 0.9823 0.9869 2.704 2.847 2.970 3.078 3.472 3.735 0.419 0.373 0.337 0.308 0.223 0.180 1.182 1.099 1.032 0.975 0.789 0.680 1.134 1.061 1.000 0.949 0.775 0.671 0.076 0.136 0.184 0.223 0.348 0.414 1.924 1.864 1.816 1.777 1.652 1.586 0.205 0.387 0.546 0.687 1.207 1.548 5.203 5.307 5.394 5.469 5.737 5.922 0.118 0.185 0.239 0.284 0.428 0.510 1.882 1.815 1.761 1.716 1.572 1.490 0.113 0.179 0.232 0.276 0.421 0.504 1.806 1.751 1.707 1.669 1.544 1.470 25 0.9896 3.931 0.153 0.606 0.600 0.459 1.541 1.804 6.058 0.565 1.435 0.559 1.420 Source: T P Ryan, Statistical Methods for Quality Improvement © 1989 New York: John Wiley & Sons This material is used by permission of John Wiley & Sons, Inc www.downloadslide.com Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition Back Matter Statistical Tables TABLE 14 1559 5550 4735 5333 8495 1947 4785 9972 0472 4727 3658 6906 3793 3376 6126 0466 9908 7594 5715 7932 6311 0476 5317 7474 7460 1002 5449 9453 0471 5469 2782 3129 7092 9566 5863 5881 6416 9568 0452 8762 0194 3306 7198 8350 7449 6126 1851 7698 0810 6647 3867 1172 6701 8244 8009 1947 9562 0729 6904 Random Numbers 9068 6245 6214 1313 2956 3353 6325 9163 4629 6994 3226 9758 6916 5966 0224 7566 9832 3636 9301 4739 2025 1624 3903 8876 6800 1494 6891 0809 2725 2668 9603 7217 9885 0501 7000 9151 9939 3012 9538 5920 0270 5478 3079 4846 4279 5399 7940 4218 0118 7149 7111 7278 1668 0620 4031 8315 4821 9026 2569 9290 7313 8037 3063 1121 1197 1868 5833 2007 1175 5981 0244 0132 1614 7169 1320 8185 1224 5847 4567 5250 3470 6098 1918 1987 9972 9047 7151 7588 1996 1877 5020 3714 8352 1714 2321 9569 6316 5730 8989 7601 2797 2171 1309 4224 0852 9908 2726 4979 1409 5549 7527 5067 8736 7884 9755 8050 9631 3251 8303 0117 1385 1134 8484 7363 5020 0100 4464 5622 9025 0259 8873 4025 3596 8777 8835 6808 3524 6797 6099 1600 9438 9828 2758 3877 6297 9982 6573 2249 4159 3788 8557 1062 9276 3147 0439 9065 1893 4777 0342 1605 6972 0612 1018 5491 3860 5130 0458 6809 9439 2492 0413 2649 2215 7187 0106 8096 0079 8508 7652 1882 8676 2920 9003 9100 5758 3312 2341 1080 4609 8987 0721 1593 8470 0384 1184 0077 4540 6718 0675 3482 2061 0737 6104 1075 0411 0546 3857 9809 0853 7804 0634 7218 6755 1705 0710 1186 2169 3897 4996 0928 4584 2496 6557 1536 3132 1059 3313 3427 6211 7961 1429 2382 4074 2782 8906 8838 8954 5069 0828 6241 7934 9313 0823 3696 8728 8562 1437 1269 4975 1537 5097 5448 3699 3404 6674 8488 7539 3261 5505 6664 6880 4006 7762 1120 0110 6637 2570 9465 9524 2401 6922 2510 4680 2158 9245 7073 4133 0023 6599 4988 2091 4946 8011 1722 5739 0082 9793 9457 7825 6253 1931 4743 4665 5713 8738 1051 6354 2957 9960 0670 3434 7379 6496 1193 5192 6721 5957 4814 6695 7286 9575 1272 6752 8061 3639 9681 7749 5167 0391 1500 0477 8091 6129 6132 8010 4544 2186 6228 0379 1032 5759 9881 1639 6558 7082 7650 9780 9328 4642 9750 9918 4314 8592 7919 9024 3071 5120 9261 4181 1252 6669 9436 3212 8503 871 © The McGraw−Hill Companies, 2009 Appendix C: Statistical Tables 6677 7668 0530 5304 5263 4261 7391 6297 2497 1471 7331 7556 2098 6090 2686 4669 1181 4391 5438 9777 3204 4195 9993 9170 5763 0669 7153 5090 1224 1701 0544 3945 7774 1697 4838 6947 7071 9149 9562 9495 9228 9429 0597 4430 6086 1541 7269 9662 4557 7477 6651 4903 8572 8120 8088 6060 4973 8854 6333 6415 1096 9210 1582 0968 0066 1250 5653 4219 7206 0792 1975 6683 8083 1796 1402 8627 2016 6508 1621 9637 2660 8191 2776 2061 8557 8881 2053 3124 3141 2660 1696 6674 7153 1954 7102 9596 4848 8534 1594 5558 3937 5948 9481 1955 7894 7047 4795 0245 7320 4267 1023 0634 6500 2490 2319 4879 3435 0952 0342 5780 0177 6198 0069 2714 5501 7782 5339 2027 5383 7898 0901 5450 1150 3905 1968 6167 9673 7244 1091 2150 8488 4025 9373 0513 3367 7570 6563 6147 6737 2286 2775 6208 1680 0097 8758 8634 9321 8600 3597 7573 5753 9048 9860 1843 0382 7718 4861 5822 8099 5745 1140 8127 9122 0635 8900 4206 1641 Source: T P Ryan, Statistical Methods for Quality Improvement © 1989 New York: John Wiley & Sons This material is used by permission of John Wiley & Sons, Inc 791 www.downloadslide.com 872 Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition Back Matter Index © The McGraw−Hill Companies, 2009 INDEX Page numbers followed by n indicate material found in notes A Absolute frequencies, 21 Absolute kurtosis, 22 Absolute zero, Acceptable Pins (case), 177–178 Acceptance sampling, 602 Acceptance Sampling of Pins (case), 216 Actions, 703 Aczel, A D., 88n, 731n Additive factors, 381, 568 Adjusted multiple coefficient of determination, 479 Aizenman, Joshua, 565n All possible regressions, 545 Alternative actions, 704 Alternative hypothesis, 257–258, 353–354 Analysis of covariance, 509 Analysis of variance (ANOVA), 205, 349–402, 509 ANOVA diagram, 371 ANOVA table and examples, 364–369 ANOVA table for regression, 443–444 assumptions of, 351 blocking designs, 379 completely randomized design, 379 computer use and, 398–402 confidence intervals, 372–373 defined, 349 degrees of freedom, 361–362 error deviation, 357 Excel for, 398–399 experimental design, 379 F statistic, 363–364 fixed-effects vs random-effects models, 379 further analysis, 371–373 grand mean, 355, 359 hypothesis test of, 350–354 main principle of, 355 mean squares, 362–363 MINITAB for, 400–402 models, factors, and designs, 378–380 multiple regression, 475, 480 one-factor model, 378 one-factor vs multifactor models, 378–379 principle of, 357 quality control and, 602 random-effects model, 379 randomized complete block design, 379, 393–395 repeated-measures design, 395 sum-of-squares principle, 358–361 template (single-factor ANOVA), 377 test statistic for, 351–354, 364 theory and computations of, 355–358 three factors extension, 389 total deviation of data point, 359 treatment deviation, 357 Tukey pairwise-comparisons test, 373–376 two-way ANOVA, 380–381 two-way ANOVA with one observation per cell, 389–391 unequal sample size, 376 ANOVA; see Analysis of variance (ANOVA) ANOVA table, 364–369 ANOVA test statistic, 351–354, 364 Arithmetic mean, 10 Asimov, Eric, 219 Auto Parts Sales Forecasts (case), 592–593 Autocorrelation, 539 Average, 10; see also Mean Averaging out and folding back, 707 B Backward elimination, 545–546 Bailey, Jeff, 669n Baker-Said, Stephanie, 626n Balanced design, 376 Baland, J M., 482n Banner, Katie, 317n Bar charts, 25, 38 probability bar chart, 92–93 Barbaro, Michael, 284n Barenghi, C., 731n Barr, Susan Learner, 254n Barrionuevo, Alexei, 185n Base period, 584 Basic outcome, 54 Bayes, Thomas, 73 Bayes’ Theorem, 73–74, 689 additional information and, 714–716 continuous probability distributions, 695–700 determining the payoff, 716 determining the probabilities, 716–719 discrete probability models, 688–693 extended Bayes’ Theorem, 77–79 normal probability model, 701–702 Bayesian analysis, 687–688 Bayesian statistics, 687–699 advantages of approach, 691 classical approaches vs., 688 computer usage for, 731–733 subjective probabilities, evaluation of, 701–702 template for, 692–693 Bearden, William O., 377n Beaver, William H., 443n Bell-shaped normal curve, 147 Berdahl, Robert M., 51 Berenson, Alex, 713n Bernoulli, Jakob, 112 Bernoulli distribution, 112 Bernoulli process, 113 Bernoulli random variable, 112 Bernoulli trial, 112 Bertrand, Marianne, 519n Best, R., 731n Best linear unbiased estimators (BLUE), 415, 472 B computation of, 269–271 B and power of test, 264, 289 Between-treatments deviation, 360 Bias, 181, 201–203 nonresponse bias, 5–6, 181 Bigda, Caroline, 25n Billett, Matthew T., 512n Binary variable, 504 BINOMDIST function, 133 Binomial distribution, 71, 115 MINITAB for, 134–135 negative binomial distribution, 118–120 normal approximation of, 169–170 population proportions, 276 template for, 115–116 Binomial distribution formulas, 114–115 Binomial distribution template, 115–116 Binomial probability formula, 114 Binomial random variable, 93, 113–116 conditions for, 113–114 Binomial successes, 184 Biscourp, Pierre, 493n Block, 393, 653 Blocking, 308 Blocking designs, 379, 393–397 randomized complete block design, 393–395 repeated-measures design, 395 BLUE (best linear unbiased estimators), 415, 472 Bonferroni method, 376 Box-and-whisker plot, 31 Box plots, 31–33, 38 elements of, 31–32 uses of, 33 Brav, James C., 481n 793 www.downloadslide.com Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition 794 Back Matter Index © The McGraw−Hill Companies, 2009 Index Briley, Donnel A., 370n Brooks, Rick, 284n Bruno, Mark, 645n Bukey, David, 318n Burros, Marian, 644n Bush, Jason, 227n Business cycle, 566, 621 C c chart, 614–615 Caesar, William K., 569n Callbacks, 189 Capability of any process, 598 Capital Asset Pricing Model (CAPM), 458 Carey, John, 316n Carlson, Jay P., 377n Carter, Erin, 632n Cases Acceptable Pins, 177–178 Acceptance Sampling of Pins, 216 Auto Parts Sales Forecasts, 592–593 Checking Out Checkout, 406 Concepts Testing, 145 Firm Leverage and Shareholder Rights, 466–467 Job Applications, 89 Multicurrency Decision, 177–178 NASDAQ Volatility, 48 New Drug Development, 736–737 Nine Nations of North America, 684–685 Pizzas “R” Us, 735 Presidential Polling, 254–255 Privacy Problem, 255 Quality Control and Improvement at Nashua Corporation, 618–619 Rating Wines, 406 Return on Capital for Four Different Sectors, 556–558 Risk and Return, 467 Tiresome Tires I, 301 Tiresome Tires II, 346 Casey, Susan, 345n Cassidy, Michael, 652n Categorical variable, Causality, 433 Center of mass, 103 Centerline, 599, 606, 608–609, 612, 614 Central limit theorem, 194–198, 220 effects of, 195 history of, 198 population standard deviation and, 198 sample size and, 194 Central tendency; see Measures of central tendency Centrality of observations, 10, 102 Chance node, 705 Chance occurrences, 703–704 Chance outcome, 715 Chart Wizard, 37 Charts; see Methods of displaying data Chatzky, Jean, 171, 254n, 297n, 644n Chebyshev’s theorem, 24, 108–109 Checking Out Checkout (case), 406 Chi-square analysis with fixed marginal totals, 675 Chi-square distribution, 239, 249, 330 mean of, 239 values and probabilities of, 240 Chi-square random variable, 331 Chi-square statistic, 662 Chi-square test for equality of proportions, 675–678 Chi-square test for goodness of fit, 661–668 chi-square statistic, 662 degrees of freedom, 665–666 multinominal distribution, 662–663 rule for use of, 665 steps in analysis, 661 template for, 664, 668 unequal probabilities, 664–666 CHIINV function, 249 Christen, Markus, 377n, 481n, 555n Classes, 20 Classical approach, 687–688 Classical probability, 52 Cluster, 188 Cluster sampling, 188 Coefficient of determination (r ), 439–442 Collinearity, 531–532; see also Multicollinearity Combinations, 71, 81 Combinatorial concepts, 70–72 Comparison of two populations, 303–341 computer templates for, 338–340 difference (population-means/independent random samples), 310–322 equality of two population variances, 333–337 F distribution, 330–333 large-sample test (two population proportions), 324–328 paired-observation comparisons, 304–308 Complement, 53–54 rule of complements, 58 Completely randomized design, 352, 379 Computational formula for the variance of a random variable, 105 Computers; see also Excel; Templates bar charts, 38 Bayesian statistics/decision analysis, 731–733 box plots, 38 confidence interval estimation, 248–250 decision analysis, 731–733 for descriptive statistics and plots, 35–40 in forecasting and time series, 588–591 histograms, 36–37 hypothesis testing, 298–300 multiple regression using Solver, 548–551 normal distribution, 171–172 one-way ANOVA, 398 paired-difference test, 338–340 percentile/percentile rank computation, 36 pie charts, 37 probability, 80–82 for quality control, 616–617 sampling distributions, 209–213 scatter plots, 38–39 for standard distributions, 133–134 time plots, 38 two-way ANOVA, 398–399 Concepts Testing (case), 145 Concomitant variables, 509 Conditional probability, 61–63, 74, 688, 715 Confidence, 219 Confidence coefficient, 223 CONFIDENCE function, 248 Confidence intervals, 167, 219–250, 303 Bayesian approach, 220n classical/frequentist interpretation, 220n defined, 219 80% confidence interval, 224 Excel functions for, 248–250 expected value of Y for given X, 457 half-width, determining optimal, 245–246 important property of, 224 individual population means, 372 MININTAB for, 249–250 95% confidence interval, 221–223 paired-observation comparisons, 307–308 population mean (known standard deviation), 220–226 population means, difference between, 316, 321 population proportion (large sample), 235–237 population proportions, difference between, 327 population variance, 239–242 regression parameters, 426–428 sample-size determination, 243–245 t distribution, 228–233 templates, 225–226, 242 Confidence level, 223, 263 Conlin, Michelle, 288n Consistency, 203 Consumer price index (CPI), 561, 583, 585–587 Contingency table, 62, 669–670 Contingency table analysis, 669–672 chi-square test for independence, 669–672 chi-square test statistic for independence, 670 degrees of freedom, chi-square statistic, 670 expected count in cell, 671 hypothesis test for independence, 670 template, 672–673 Yates correction, 672 873 www.downloadslide.com 874 Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition Back Matter © The McGraw−Hill Companies, 2009 Index Index Continuity correction, 169–170 Continuous probability distributions, Bayes’ theorem and, 695–700 Continuous random variable, 95–96, 126–128 Control chart, 598–601, 606 centerline, 599, 606, 608–609, 612, 614 lower control limit (LCL), 599, 606, 608–609, 612, 614 out of control, 599 for process mean, 606 for process proportion, 612 upper control limit (UCL), 599, 606, 608–609, 612, 614 Control treatment (placebo), 350 Cook, R Dennis, 514n Cordoba, Jose de, 329 Correlation, 429–433, 531 Correlation analysis, 429 Correlation coefficient, 429 Correlation matrix, 533–534 Counts of data points, 21 Covariance, 430 CPI (Consumer price index), 561, 583, 585–587 Creamer, Matthew, 364n Credible sets, 689, 698–699 Creswell, Julie, 100n Crockett, Roger O., 84n Cross-product terms, 517–519 Cross-tabs, 669 Cumulative distribution function, 96–98 Cumulative frequency plots (ogives), 25, 27 Cumulative probability function, 97 Curved trends, 562 Curvilinear relationship, 413, 447–448 Cveykus, Renee, 632n Cycle, 566 Cyclical behavior, 566–569 Cyclical variation, 566 D Darwin, Charles, 409 Dash, Eric, 252n Data, 3, grouped data, 20–22 Data collection, Data set, 5, 102 Data smoothing, 570 de Fermat, Pierre, 52 de Finetti, Bruno, 52n de Mère, Chevalier, 52 de Moivre, Abraham, 52, 148, 198 Decision, 182, 704, 706 Decision analysis, 688, 702–705 actions, 703 additional information, 704 chance occurrences, 703–704 decision, 704 decision tree, 705–712 elements of, 703 final outcomes, 704 overview of, 702–705 payoff table, 706–709 probabilities, 704 utility, 725–728 value of information, 728–731 Decision node, 705 Decision tree, 705–712 Deflators, 585 DeGraw, Irv, 481n Degree of linear association, 429–431 Degrees of freedom (df), 198, 205–208 ANOVA and, 361–362, 383–384, 389 chi-square statistic, 670 chi-square tests, 665–666 sum-of-squares for error (SSE), 362 sum-of-squares total (SST) and, 362 sum-of-squares for treatment (SSTR), 362 Degrees of freedom of the denominator, 330 Degrees of freedom of the numerator, 330 Demers, Elizabeth, 465n Deming, W Edwards, 596–597 Deming Award, 596 Deming’s 14 Points, 597–598 Dependent indicator variable, regression with, 528–529 Dependent variable, 409 Descriptive graphs, 25 Descriptive statistics, 3–40, 181n computer use for, 35–39 exploratory data analysis, 29–33 grouped data and histogram, 20–22 mean-standard deviation relations, 24–25 measures of central tendency, 10–14 measures of variability, 10–14 methods of displaying data, 25–29 MINITAB for, 39–40 percentiles and quartiles, 8–9, 36 random variable, 91–94 skewness and kurtosis, 22–23, 33 templates for random variables, 109–110 Deseasonalizing a time series, 572–573 df; see Degrees of freedom (df) Diffuse priors, 698 Discrete probability models, 688–689 Discrete random variable, 95–96 Bayes’ theorem for, 689 cumulative distribution function of, 97 expected values of, 102–107 probability distribution of, 96 variance of, 104–105 Disjoint sets, 54 Dispersion, 14–15, 106; see also Measures of variability Displaying data; see Methods of displaying data Distribution of the data, Distribution-free methods, 682; see also Nonparametric tests 795 Distributions; see also Normal distribution; Probability distribution Bernoulli distribution, 112 cumulative distribution function, 96–98 exponential distribution, 130–133 geometric distribution, 120–121 hypergeometric distribution, 121–124 kurtosis of, 22–23 Poisson distribution, 124–126 sampling distributions, 190–200 skewness of, 22–23 uniform distribution, 129–130 Dobyns, L., 601n Dow Jones Industrial Average, 582–583 Dummy variable, 503, 507, 568 Dummy variable regression technique, 568 Durbin-Watson test, 445, 539–541 Durbin-Watson test statistic, 540 E Eccles, Robert G., 577n EDA (Exploratory data analysis), 29–33 Efficiency, 201, 203, 733 80% confidence interval, 224 Elementary event, 54 Elements of a set, 53 Elliot, Stuart, 324n Empirical rule, 24–25, 163n Empty set, 53 Enumerative data, 661 Epstein, Edward, 68n Error deviation, 357, 359 Error probability, 223 Estimated regression relationship, 472 Estimators, 183–184, 201 consistency of, 201, 203 efficiency of, 201, 203 of population parameter, 184–185 properties of, 201–204, 414 sufficiency of, 201, 203 as unbiased, 201–203 Event, 55, 688 EVPI (expected value of perfect information), 728 Excel; see also Solver Macro ANOVA and, 398–399 Bayesian revision of probabilities, 80–81 descriptive statistics and plots, 25–40 F-test, 340 in forecasting and time series, 588–591 graphs, 27 histograms, 36–37 LINEST function, 461–462 normal distribution, 171–172 one-sample hypothesis testing, 298–299 paired-difference test, 338–340 percentile/percentile rank computation, 36 probabilities, 80–82 Random Number Generation analysis, 211 www.downloadslide.com Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition 796 Back Matter © The McGraw−Hill Companies, 2009 Index Index Excel; see also Solver Macro—Cont regression, 458–459, 462–463 Sampling analysis tool, 210 sampling distributions and, 209–213 standard distributions and, 133–134 t-test, 340 Excel Analysis Toolpack, 35 Expected net gain from sampling, 730 Expected payoff, 707, 711–712 Expected value of a discrete random variable, 102–103 Expected value of a function of a random variable, 103–104 Expected value of a linear composite, 107 Expected value of a linear function of a random variable, 104 Expected value of perfect information (EVPI), 728 Expected value of sample mean, 192 Expected value of the sum of random variables, 107 Experiment, 54 Experimental design, 379, 602 Experimental units, 308, 380 Explained deviation, 439–440 Explained variation, 361, 440 Exploratory data analysis (EDA), 29–33 box plots, 31–33 stem-and-leaf displays, 30–31 EXPONDIST function, 134 Exponential distribution, 130–133 common examples of, 130–131 remarkable property of, 131 template for, 131–132, 134 Exponential model, 524 Exponential smoothing methods, 577–582 model for, 579 template for, 581–582 weighting factor (w), 578–580 Extended Bayes’ Theorem, 77 Extra sum of squares, 543 Extrapolation, 498 Factorial, 70, 81 Fair games, 103 Fairley, W., 257n Farley, Amy, 99n Farzad, R., 43n Fass, Allison, 234n, 288n Feller, W., 70, 198, 626 Ferry, John, 29n, 69n Fialka, John J., 251n 50th percentile, Final outcomes, 704 Firm Leverage and Shareholder Rights (case), 466–467 First quartile, Fisher, Anne, 252n Fisher, Sir Ronald A., 330, 349 Fixed-effects vs random-effects models, 379 Flight simulators, 30 Fong, Eric A., 465n Forbes, Malcolm, Forbes, Steve, 701n Forecasting Excel/MINITAB in, 588–591 exponential smoothing methods, 577–582 index numbers, 582–587 multiplicative series, 576–577 ratio-to-moving-average method, 569–576 seasonality and cyclical behavior, 566–569 trend analysis, 561–564 Forward selection, 545 Frame, 8, 186 Frequency, 20 Frequency distribution, 183 Frequency polygon, 25–27 Frequentist approach, 687 Friedman test, 396, 645 data layout for, 653 null and alternative hypotheses of, 653 template, 655–656 test statistic, 654 Fulcrum, 11 Full model (F test), 542–543 F G F distribution, 330–333, 351, 444 degrees of freedom of the denominator, 330, 351 degrees of freedom of the numerator, 330, 351 equality of two population variances, 333–334 templates for, 336–337 F ratio, two-way ANOVA, 384 F statistic, 363–364 F test, 314, 340 multiple regression model, 473–476 partial F tests, 542–544 of regression model, 443–444, 448 Factor, 378 Gagnepain, Philippe, 582n Galilei, Galileo, 52 Galton, Sir Francis, 409 Gambling models, 52 Ganguly, Ananda, 393n Garbaix, Xavier, 481n Gauss, Carl Friedrich, 148 Gauss-Markov theorem, 415 Gaussian distribution, 148 Generalized least squares (GLS), 541 Geometric distribution, 120–121 formulas for, 120 template for, 121 Geometric progression, 120 Gleason, Kimberly C., 466n, 491n GLS (Generalized least squares), 541 Goal seek command, 116, 123, 166 Goldstein, Matthew, 639n Gomez, Paulo, 565n Good, I J., 51 Goodness-of-fit test, 662 for multinomial distribution, 663–664 Goodstein, Laurie, 6n Gossett, W D., 229 Grand mean, 355, 359, 378, 383, 599 Graphs; see Methods of displaying data Gray, Patricia B., 253n Green, Heather, 239n Grouped data, 20–22 Grover, Ronald, 225n Gruley, Bryan, 144n H Hall, Kenji, 238n Hammand, S., 26 Hansell, Saul, 288n Hardesty, David M., 377n Harris, Elizabeth, 201n, 280n Harris, Marlys, 280n, 285n HDP (highest-posterior-density), 698 Hellmich, Nancy, 69n Helm, Burt, 87n, 189n, 679n Herbold, Joshua, 393n Heteroscedasticity, 446, 494, 502, 527 Highest-posterior-density (HPD), 698 Hinges (of box plot), 31–32 Histogram, 20–22, 25, 36–37, 126–127, 449 Holson, Laura M., 309n Homogeneity, tests of, 675 Hovanesian, Marader, 44n HSD (honestly significant differences) test, 373 Huddleston, Patricia, 465n Hui, Jerome Kueh Swee, 403n Hypergeometric distribution, 121–124 formulas for, 122–123 problem solving with template, 123–124, 134 schematic for, 122 HYPGEOMDIST function, 134 Hypothesis, 257 Hypothesis testing, 257–300, 303 alternative hypothesis, 257–258, 353–354 ANOVA, 350–354 association between two variables, 658 B and power of test, 264 common types of, 272 computing B, 269 concepts of, 260–265 confidence level, 263–264 evidence gathering, 260 Excel/MINITAB for, 298–300 for independence, 670 individual regression slope parameters, 484 Kruskal-Wallis test, 646 875 www.downloadslide.com 876 Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition Back Matter © The McGraw−Hill Companies, 2009 Index Index left-tailed test, 267–270 linear relationship between X and Y, 435 median test, 677 null hypothesis, 257–258, 353–354 one-tailed and two-tailed tests, 267–269 operating characteristic (OC) curve, 292–293 optimal significance level, 263–264 p-value, 261–262, 273 p-value computation, 265–267 paired-observations two-sample test, 639 population means, 272–273, 289–290 population proportions, 276–278, 294–295 population variance, 278–279 power curve, 291–292, 296 power of the test, 264 pretest decisions, 289–296 regression relationship, 434–438, 474 required sample size (manual calculation), 290–291, 295 right-tailed test, 268, 271 sample size, 264–265, 295 significance level, 262–263 t tables, 273 templates, 274–275 test statistic, 272 two-tailed test, 267, 269, 271 two-way ANOVA, 382–383, 386 type I/II errors, 260–261, 263–264 Intercept, 418, 420 Interquartile range (IQR), 9, 14–15, 32 Intersection, 53–54 Intersection rule, 67 Interval estimate, 184 Interval scale, Intrinsically linear models, 521 Introduction to Probability Theory and Its Applications (Feller), 626 Inverse transformation, 157, 162–165 Irregular components models, 591 J Jiraporn, Pornsit, 466n, 491n Jo, Hoje, 492n Job Applications (case), 89 Johar, Gita Venkataramani, 391n Johnson, George, 687, 687n Johnston, J., 535n Joint confidence intervals, 427 Joint density, 695 Joint hypothesis, 350 Joint probability, 59 Joint probability table, 79–80 Joint test, 350 Joos, Philip, 465n Josephy, N H., 88n Juran, J M., 601 I K Ihlwan, Moon, 238n Independence of events, 66–68, 669; see also Contingency table analysis conditions for, 66 product rules for, 66–68 Independent events, 68 Independent variable, 409 Index, 582 Index numbers, 582–587 changing base period of index, 584 Consumer Price Index (CPI), 561, 583, 585–587 as deflators, 585 template, 587 Indicator variable, 503–504, 506 Indifference, 727 Inferential statistics, 52, 181 Influential observation, 498 Information, expected net gain from sampling, 730 expected value of perfect information (EVPI), 728 qualitative vs quantitative, value of, 728–731 Initial run, 604 Inner fence, 32 Interaction effects, 381–382, 510 Interarrival time, 131 k-variable multiple regression model, 469–473 Kacperczyk, Marcin, 371n Kang, Jun-Koo, 674n Kendall’s tau, 659 Keynes, John Maynard, Kim, Yongtae, 492n Kimball’s inequality, 388 King, Tao-Hsien Dolly, 512n Kirkland, R., 29n Knapp, Volker, 235n, 283n Knox, Noelle, 343n Kondratieff definition, 621 Kramarz, Francis, 493n Kranhold, Kathryn, 251n Krishnamurthy, Arvind, 481n Kroll, Lovisa, 234n, 288n Kruskal-Wallis test, 351, 378, 645–651 further analysis, 650–651 template for, 648–649 test statistic, 646 Kurtosis, 22–23 Kwon, Young Sun, 371n L Lack of fit, 498–499 Lamey, Lien, 414n 797 Large sample confidence intervals for population proportion, 324 Large-sample properties, 628 Lav, Kong Cheen, 555n Law of total probability, 73–75 LCL (lower control limit), 599, 606, 608–609, 612, 614 Least-squares estimates, 471–472, 497 Lee, Alan J., 514n Lee, Hyun-Joo, 465n Lee, Louise, 679n Lee, Yeonho, 565n Left-skewed distribution, 22 Left-tailed test, 267–270, 622 Lehman, Paula, 679n Leptokurtic distribution, 23 Lerner, Josh, 555n Lettav, Martin, 465n Level of significance, 262–264 Li, Peter Ping, 713n Likelihood function, 688–689 Linear composite, 107–110 expected value of, 107 LINEST function, 461–462, 550–551 Literary Digest presidential poll, 181–183 Lo, May Chiun, 403n Location of observations, 10, 102 Logarithmic model, 525 Logarithmic transformation, 521–523, 528 Logistic function, 528–529 Logistic regression model, 528 Loss, 704 Loss function, 603 Lower control limit (LCL), 599, 606, 608–609, 612, 614 Lower quartile, M Malkiel, Burton G., 201n Mann-Whitney U test, 314, 633–638 computational procedure, 634 MINITAB for, 637–638 null and alternative hypothesis for, 633 U statistic, 634 Manual recalculation, 502–503 Marcial, Gene G., 216n Margin of error, 221 Marginal probabilities, 80 Marketing research, Martin, Mitchell, 161n Martinez, Valeria, 577n Mauer, David, 512n Mean, 10–13, 102 defined, 10 extreme observations and, 12 grand mean, 355 population mean, 11, 15, 183, 372 sample mean, 10, 191, 193, 355 standard deviation and, 24–25 www.downloadslide.com Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition 798 Back Matter © The McGraw−Hill Companies, 2009 Index Index Mean square error (MSE), 362–363 multiple regression, 477–478 simple linear regression, 424 Mean square treatment (MSTR), 362–363 Mean time between failures (MTBF), 130 Measurements, scales of, Measures of central tendency, 10–14 mean, 10–13 median, 9–13 mode, 10–13 Measures of variability, 14–19, 102 interquartile range, 9, 14–15 range, 15 standard deviation, 15 variance, 15 Median, 9–12 Median test, 677–678 Mehring, James, 323n Method of least squares, 415 Methods of displaying data, 25–29 bar charts, 25 cautionary note to, 27–28 exploratory data analysis (EDA), 29–33 frequency polygons, 25–27 histogram, 20–22, 25, 36–37 ogives, 25–27 pie charts, 25, 37 time plots, 28 Middle quartile, MINITAB ANOVA and, 400–402 comparison of two samples, 340–341 confidence interval estimation, 249–250 for descriptive statistics/plots, 39–40 for factorial, combination, and permutation, 81 in forecasting and time series, 589–591 Mann-Whitney test, 637 multicollinearity, 533 multiple regression, 551–554 nonparametric tests, 680–681 normal distribution, 172 one-sample hypothesis testing, 299–300 for quality control, 616–617 regression analysis, 498 sampling distributions, 212–213 simple linear regression analysis, 463–464 standard distributions, 134–135 stepwise regression, 547–548 Missing variables test, 446 Mode, 10–13, 22 Montgomery, D., 502n Moskin, Julia, 43n Mosteller, F., 257n Mound-shaped distribution, 24 Moving average, 569 MSE; see Mean square error (MSE) MSTR (mean square treatment), 362–363 MTBF (mean time between failures), 130 Mukhopadhyay, Anirban, 391n Multicollinearity, 483–484, 531–537 causes of, 515, 532–533 detecting existence of, 533–536 effects of, 536 solutions to problem, 537 Multicollinearity set, 532 Multicurrency Decision (case), 177–178 Multifactor ANOVA models, 378–379 Multinomial distribution, 662 goodness-of-fit test for, 663 Multiple coefficient of determination (R ), 478 Multiple correlation coefficient, 478 Multiple regression, 409, 469–554 adjusted multiple coefficient of determination, 479 ANOVA table for, 475, 480 assumptions for model, 469 cross-product terms, 517–519 decomposition of total deviation, 474 dependent indicator variable and, 528–529 Durbin-Watson test, 539–541 estimated regression relationship, 472–473 F test, 473–476 how good is the regression, 477–480 influential observation, 498 k-variable model, 469–473 lack of fit and other problems, 498–499 least-squares regression surface, 472 LINEST function for, 550–551 mean square error (MSE), 477 measures of performance of, 480 MINITAB and, 551–552 multicollinearity, 483–484, 531–537 multiple coefficient of determination R 2, 478–479 multiple correlation coefficient, 478 nonlinear models and transformations, 521–529 normal equations, two independent variables, 470 normal probability plot, 496 other variables, 517–519 outliers and influential observations, 496–498 partial F test, 542–544 polynomial regression, 513–519 prediction and, 500–503 qualitative independent variables, 503–511 qualitative/quantitative variables interactions, 510–511 residual autocorrelation, 539–541 residual plots, 494 significance of individual regression parameters, 482–491 Solver, 548–551 standard error of estimate, 478 standardized residuals, 494–497 template for, 472, 487, 490, 496, 502, 516 validity of model, 494–499 variable selection methods, 545–547 Multiplicative model, 521, 568 Multiplicative series, forecast of, 576–577 Multistage cluster sampling, 188 Murphy, Dean E., 51n Mutually exclusive events, 59, 68–69 Mutually independent, 107 N N factorial (n!), 70 NASDAQ Volatility (case), 48 Negative binomial distribution, 118–120 problem solving with template, 119–120, 134 Negative correlation, 430 Negative skewness, 22 NEGBINOMDIST function, 134 Nelson, Lloyd S., 605n, 619n Nelson, Melissa, 652n Net regression coefficients, 471 New Drug Development (case), 736–737 Newquiest, Scott C., 577n Newton, Sir Isaac, 595 Nine Nations of North America (case), 684–685 95% confidence interval, 221–223 Nominal scale, Noninformative, 687 Nonlinear models, 513, 521–529 Nonparametric tests, 314, 621–682 chi-square test, 661–662 chi-square test for equality of proportions, 675–677 contingency table analysis, 669–673 defined, 621 Friedman test, 653–656 Kruskal-Wallis test, 351, 645–651 Mann-Whitney U test, 633–638 median test, 677–678 MINITAB for, 680–681 paired-observations two-sample test, 639–640 runs test, 626–629 sign test, 621–625 Spearman rank correlation coefficient, 657–660 summary of, 682 Wald-Wolfowitz test, 630–631 Wilcoxon signed-rank test, 639–643 877 www.downloadslide.com 878 Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition Back Matter © The McGraw−Hill Companies, 2009 Index Index Nonresponse, 188–189 Nonresponse bias, 5–6, 181 Normal approximation of binomial distributions, 169–170 template, 171–172 Normal distribution, 147–172; see also Standard normal distribution absolute kurtosis of, 23 Excel functions for, 171–172 inverse transformation, 162–165 MINITAB for, 172 normal approximation of binomial distributions, 169–170 probability density function, 147 properties of, 148–150 sampling and, 192, 198 standard normal distribution, 151–155 template for, 166–169 testing population proportions, 276 transformation of normal random variables, 156–160 Normal equations, 417 Normal prior distribution, 701–702 Normal probability model, 696, 702 Normal probability plot, 448–450, 496 Normal random variables inverse transformation, 162–165 inverse transformation of Z to X, 157 obtaining values, given a probability, 165 transformation of X to Z, 156, 160 transformation of, 156–160 using the normal transformation, 157 Normal sampling distribution, 192–193 NORMDIST function, 171 NORMSINV function, 249 Null hypothesis, 257, 353–354 Chi-square test for equality of proportions, 675 of Friedman test, 653 Mann-Whitney U test, 633 multinomial distribution, 663 O Objective probability, 52 OC (Operating characteristic curve), 292 Odds, 58 Ogives, 25–27 standard deviation, 24 One-factor ANOVA model, 378 Excel/MINITAB for, 398, 401 multifactor models vs., 378–379 One-tailed test, 267–268 One-variable polynomial regression model, 514 Operating characteristic curve (OC curve), 292–293 Optimal decision, 733 Optimal sample size, 301 Optimal value, 602 Ordinal scale, Ordinary least squares (OLS) estimation method, 494 Out of control process, 599 Outcomes, 54 Outer fence, 32 Outliers, 12, 33, 496–498 P p chart, 611–612 template for, 612–613 p-value, 261–262, 273, 319, 321 computation of, 265–267 definition of, 262 test statistic, 266 Paired-observation comparisons, 304–308 advantage of, 304 confidence intervals, 307–308 Excel for, 338–340 template for, 306–308 test statistic for, 305 Paired-observation t test, 304–306 Paired-observations two-sample test, 639 Palmeri, Christopher, 344n Parameters, 184, 682 Pareto diagrams, 601 template for, 603 Park, Myung Seok, 492n Parsimonious model, 410 Partial F statistic, 543 Partial F tests, 542–544 Partition, 73–74 Pascal, Blaise, 52 Passy, Charles, 253n Payoff, 704, 716 Payoff table/matrix, 706–709 Pearson product-moment correlation coefficient, 430, 658 Peck, F., 502n Peecher, Mark E., 393n People v Collins, 257 Percentile, 8–9, 36 Percentile rank computation, 36 Pereira, Pedro, 582n Permutations, 71, 81 Personal probability, 53 Peters, Ruth, 144n Phav, Ian, 555n Pie chart, 25, 37 Pissaeides, Christopher A., 476n Pizzas “R” Us (case), 735 Platykurtic distribution, 23 Point estimate, 184 Point predictions, 454–455 799 Poisson distribution, 124–126, 614 formulas for, 124–125 problem solving with template, 125–126, 134 Poisson formula, 124–125 POISSON function, 134 Polynomial regression, 513–519 Pooling, 676 Population, 5, 181, 191, 349 defined, 5, 183 sampling from the, 5, 67, 181 Population correlation coefficient, 429–430 Population intercept, 411 Population mean, 11, 15, 183 cases not covered by Z or t, 314 confidence interval, 372 confidence interval (known standard deviation), 220–225 difference using independent random samples, 316 hypothesis tests of, 272, 289–290 population mean differences, 316 templates, 245, 275, 291 test statistic is t, 272, 313–314 test statistic is Z, 272, 311–312 Population parameter, 183–184 comparison of; see Comparison of two populations point estimate of, 184 sample statistics as estimators of, 182–186 Population proportion, 184 binomial distribution/normal distribution, 277 confidence intervals, 327 hypothesis test of, 276–278, 294 large-sample confidence intervals, 235–227 large-sample test, two population proportions, 324 manual calculation of sample size, 295 template for, 237, 294, 296, 328 test statistic for, 325 Population regression line, 413 Population simple linear regression model, 412 Population slope, 411 Population standard deviation, 16, 198 Population variance, 15 confidence intervals for, 239–241 F distribution and, 330–337 hypothesis test of, 278 statistical test for equality of, 333–336 template for, 242, 278 Positive skewness, 22 Posterior density, 696 Posterior (postsampling) information, 687 Posterior probability, 76, 688 Posterior probability distribution, 689 www.downloadslide.com Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition 800 Back Matter Index © The McGraw−Hill Companies, 2009 Index Power curve, 291–292, 296 Power of the test, 264 Prediction, 457 multiple regression and, 500–503 point predictions, 454–455 prediction intervals, 455–457, 501 simple linear regression, 454–457 of a variable, 411 Prediction intervals, 455–457, 501 Predictive probabilities, 717 Presidential Polling (case), 254–255 Pretest decisions, 289–296 Prior information, 687 Prior probabilities, 76, 688, 716 Prior probability density, 695 Prior probability distribution, 689, 698–699 Privacy Problem (case), 255 Probability, 51–84, 257 basic definitions for, 55–56 Bayes’ theorem, 75–79 classical probability, 52 combinatorial concepts, 70–72 computer use for, 80–82 conditional probability, 61–63 decision analysis, 704, 716–719 defined, 51, 57 independence of events, 66–68 interpretation of, 58 intersection rule, 67 joint probability, 59 joint probability table, 79–80 law of total probability, 73–75 marginal probabilities, 80 mutually exclusive events, 59 objective, 52 personal probability, 53 posterior probability, 76 prior probabilities, 76 probability of event A, 55 range of values, 57–58 relative-frequency probability, 52 rule of complements, 58 rule of unions, 58–59 rules for, 57–59 standard normal distribution, 151–153 subjective, 52 unequal/multinomial probabilities, 664–665 union rule, 67 Probability bar chart, 92–93 Probability density function, 127–128, 147 Probability distribution, 91, 94–95, 190; see also Normal distribution cumulative distribution function, 96–98 discrete random variable, 96 mean as center of mass of, 103 Probability theory, 51–52 Process capability, 598 Process capability index, 176 Product rules, 66 Product rules for independent events, 67–68 P th percentile, Q Qualitative independent variables, 503–511 Qualitative information, Qualitative variable, 4, 503 defined, quantitative variable interactions, 510–511 Quality control, 595 Quality control and improvement, 595–617 acceptance sampling, 602 analysis of variance, 602 c chart, 614–615 control charts, 598–601 Deming’s 14 points, 597–598 experimental design, 602 history of, 596 p chart, 611–613 Pareto diagrams, 601, 603 process capability, 598 R chart, 608 s chart, 608–610 Six Sigma, 602 statistics and quality, 596–597 Taguchi methods, 602–603 x-bar chart, 604–607 x chart, 615 Quality Control and Improvement at Nashua Corporation (case), 618–619 Quantitative information, Quantitative variable, 4, 503, 507 defined, qualitative variable interactions, 510–511 Quartiles, 8–9 R R chart, 608–610 Ramayah, T., 403n Ramsey, Frank, 52n Random-effects model, 379 Random Number Generation (Excel), 211 Random number table, 186–187 Random sample, 5, 181, 311 Excel and, 211 obtaining a, 186–187 single random sample, Random sampling, 67 Random variables, 91–94, 186 Bayesian statistics, 689 Bernoulli random variable, 112 binomial random variable, 93, 113–114 Chebyshev’s theorem, 108–109 Chi-square random variable, 331 continuous, 95–96, 126–128 cumulative distribution function, 96–98, 128 defined, 91–92 discrete random variable, 95–96 expected values of, 102–107 exponential distribution, 130–133 geometric distribution, 120–121 hypergeometric distribution, 121–124 linear composites of random variables, 107–108 negative binomial distribution, 118–120 Poisson distribution, 124–126 standard deviation of, 106 sum and linear composites of, 107–110 templates for, 109–110 uniform distribution, 129–130 variance of, 104–106 Randomize/randomization, Randomized complete block design, 379, 393–395 repeated-measures design, 393 template for, 396–397 Range, 15 Range of values, 57–58 Rank sum test, 633 Rating Wines (case), 406 Ratio scale, Ratio to moving average, 570 Ratio-to-moving-average method, 569–576 deseasonalizing data, 572–573 quarterly/monthly data, 571 template for, 574 Trend ϩ Season forecasting, 574–576 Reciprocal model, 527–528 Reciprocal transformation, 528 Reduced model (F test), 543 Regnier, Pat, 735n Regression, 409 Regression analysis; see Multiple regression; Simple linear regression Regression deviation, 439 Regression line, 415, 424 Relative frequency, 21 Relative-frequency polygon, 26 Relative-frequency probability, 52 879 www.downloadslide.com 880 Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition Back Matter © The McGraw−Hill Companies, 2009 Index Index Relative kurtosis, 23 Repeated-measures design, 380, 395 Residual analysis, 445–450 Residual autocorrelation, 539–541 Residual plots, 494 Residuals, 378, 411 histogram of, 449 standardized residuals, 494–497 Response surface, 469 Restricted randomization, 393 Return on Capital for Four Different Sectors (cases), 555–558 Reward, 704 Rhee, Youngseop, 565n Richtel, Matt, 142n Ridge regression, 537 Right-skewed distribution, 22–23 Right-tailed test, 268, 271, 622 Rises, Jens, 569n Risk, 18 Risk-aversion, 726 Risk-neutral, 726 Risk and Return (case), 467 Risk taker, 726 Roberts, Dexter, 166 Rose, Stuart, 695n Rule of complements, 58 Rule of unions, 58–59 Run, 627 Runs test, 626–631 large-sample properties, 628–629 test statistic, 628 two-tailed hypothesis test, 628 Wald-Wolfwitz test, 630–631 Ryan, Patricia A., 481n Ryan, T P., 614n S s chart, 608–610 Sample, small vs large samples, 194, 232 Sample correlation coefficient, 430–431 Sample mean, 10, 191, 193, 355, 378 expected value of, 192 standard deviation of, 192 standardized sampling distribution of, 198 Sample proportion, 184–185, 198 Sample-size determination, 243–245, 248 hypothesis test, 264–265, 294 manual calculation of, 290–291, 295 template for, 290 Sample space, 54–55, 92 Sample standard deviation, 16 Sample statistic, 184 as estimator of population parameters, 183–186 Sample variance, 15, 17, 205 Sampling analysis tool (Excel), 210 Sampling distribution, 183, 190–200 defined, 190 MINITAB for generating, 212–213 normal sampling distribution, 192–193 sample proportion and, 198 template for, 209–210 Sampling error, 221 Sampling from the population, 5, 181 Sampling methods, 187–189 cluster sampling, 188 multistage cluster sampling, 188 other methods, 187–188 single-stage cluster sampling, 188 stratified sampling, 187 systematic sampling, 188 two-stage cluster sampling, 188 Sampling with replacement, 114 Sampling and sampling distributions, 181–213 central limit theorem, 194–198 degrees of freedom, 205–207 estimators and their properties, 201–204 expected net gain from, 730 Literary Digest sampling error, 181–183 nonresponse, 188–189 obtaining a random sample, 186–187 as population parameters estimators, 183–186 small vs large samples, 194 standardized sampling distribution of sample mean, 198 template, 209–213 uses of, 182 with/without replacement, 114 Sarvary, Miklos, 377n, 481n, 555n Scales of measurement, interval scale, nominal scale, ordinal scale, ratio scale, Scatter plots, 38–39, 409 Schank, Thorsten, 438n Schatz, Ronald, 577n Scheffé method, 376 Schnabel, Claus, 438n Schoar, Antoinette, 519n, 555n Schoenfeld, Bruce, 235n Schwartz, Nelson D., 282n Sciolino, Elaine, 70n Seasonal variation, 566 Seasonality, 566–569 multiplicative model, 568 regression model with dummy variables for, 568 Seber, George A F., 514n Seitz, Thomas, 569n 801 Semi-infinite intervals, 151 Set, 53 75th percentile, Shah, Jagar, 238n Shakespeare, Catherine, 443n Shewhart, Walter, 598 Shrum, J L., 370n Sialm, Clemens, 371n Sigma squared, 15 Sign test, 621–625 possible hypotheses for, 622 template for, 623 test statistic, 623 Significance level, 262–264 Sikora, Martin, 651n Silverman, Rachel Emma, 238n Simple exponential smoothing, 577 Simple index number, 583 Simple linear regression, 409, 411–414 analysis-of-variance table, 443–444 coefficient of determination, 439 conditional mean of Y, 412 confidence intervals for regression parameters, 426–428 correlation, 429–433 curvilinear relationship between Y and X, 413, 447–448 distributional assumptions of errors, 413 error variance, 424–428 estimation: method of least squares, 414–422 Excel Solver for, 458–460, 463 F test of, 443–444 goodness of fit, 438–442 heteroscedasticity, 446 how good is the regression, 438–442 hypothesis tests about, 434–437 linear relationship between X and Y, 435 mean square error (MSE), 424–425 MINITAB for, 463–464 missing variables test, 446 model assumptions, 412 model building, 410–411 model inadequacies, 445–450 model parameters, 412 normal equations, 417 normal probability plot, 448–450 population regression line, 413 population simple linear regression model, 412 residual analysis, 445–450 slope and intercept, 418, 427 Solver method for, 458–460 standard error of estimate, 424–428 steps in, 411 sum of squares for error (SSE), 415–417, 425 t test, 435, 444 template for, 421–422 use for prediction, 454–457 www.downloadslide.com Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition 802 Back Matter Index © The McGraw−Hill Companies, 2009 Index Single mode, 702 Single random sample, Single-stage cluster sampling, 188 Single variable, 583 Six Sigma, 602 Skedevold, Gretchen, 565n Skewness, 22–23, 33, 702 Slope, 418, 420, 435 Smith, Bill, 602 Smith, Craig S., 322n Soliman, Mark T., 443n Solver Macro, 247 multiple regression and, 548–545 regression, 458–460 Sorkin, Andrew Ross, 142n Spearman rank correlation coefficient, 657–660 hypothesis test for association, 659 large-sample test statistic for association, 658 template for, 659–660 Spread, 102 Standard deviation, 15, 102 defined, 16 mean and, 24–25 population standard deviation, 16, 198 of random variable, 106 of sample mean, 192 sample standard deviation, 16 Standard error, 192, 198 Standard error of estimate, 425–426 Standard normal distribution, 151–155 finding probabilities of, 151–153 finding values of Z given a probability, 153–155 importance of, 156 table area, 151 Standard normal probabilities (table), 152 Standard normal random variable Z, 151 Standard normal test statistic, 628 State of nature, 706 Statista, Statistic, 184 Statistical analysis, information from, Statistical control, 600 Statistical inference, 5–6, 28, 182–183, 658 business applications of, 6–7 Statistical model, 378 checking for inadequacies in, 445 for control of a variable, 411 as parsimonious, 410 for prediction of a variable, 411 steps in building, 411 to explain variable relationships, 411 Statistical process control (SPC), 599 Statistical test for randomness, 627 Statistics derivation of word, quality and, 596–603 as science of inference, 5–6, 28, 181 use of, 6–7, 147, 181, 219, 257, 303, 349, 409, 595 Stellin, Susan, 227n Stem-and-leaf displays, 30–31 Stepwise regression, 546–547 Stigler, S., 595n Stokes, Martha, 621n Stone, Brad, 60n, 287n Story, Louise, 342n Straight-line relationship, 409 Strata, 187 Stratified sampling, 187 Studentized range distribution, 373 Student’s distribution/Student’s t distribution, 228, 249 Subjective probabilities, 52, 688 evaluation of, 701–702 normal prior distribution, 701–702 Subsets, 53 Sufficiency, 203 Sum-of-squares principle, 358–362 Sum-of-squares total (SST), 360–362, 383–384 Sum of squares for error (SSE), 360–362, 384 Sum of squares for error (SSE) (in regression), 416–417, 425, 440–441, 475 Sum of squares for regression (SSR), 440–441, 475 Sum of squares for treatment (SSTR), 360–362, 384 Surveys, Symmetric data set/population, 13 Symmetric distribution, 22–23, 702 with two modes, 22–23 Systematic component, 411 Systematic sampling, 188 T t distribution, 228–233, 305, 314 t table, 273 t test statistic, 272–273, 313–314, 319–320, 340 Table area, 151–152 Taguchi, Genichi, 602 Taguchi methods, 602 Tahmincioglu, Eva, 189n Tails of the distribution, 151 Tallying principle, 30 Tang, Huarong, 443n TDIST function, 298 Templates, 36 bar charts, 38 Bayesian revision-binomial probabilities, 692–693 Bayesian revision-normal mean, 699 binomial distribution, 169–170 binomial probabilities, 115–116 box plot, 38 c chart, 615 chi-square tests, 664, 668, 673 confidence intervals, 225–226 control chart, 610, 612–613, 615 for data (basic statistics), 36 decision analysis, 731–733 exponential distribution, 131–132 exponential smoothing, 581–582 F-distribution, 336 Friedman test, 655–656 geometric distribution, 121 half-width, determining optimal, 245–246 histograms and related charts, 36–37 hypergeometric distribution, 123–124 hypothesis testing, population means, 274–275, 290–293 hypothesis testing, population proportion, 277, 294, 296 index numbers, 587 Kruskal-Wallis test, 648–649 manual recalculation, 502–503 minimum sample size, 248 multiple regression, 472, 487, 490, 496, 502, 518, 544 negative binomial distribution, 119–120 normal approximation of binomial distribution, 169–170 normal distribution, 166–169 operating characteristic (OC) curves, 292–293 optimal half-width, 245–247 paired-observation comparisons, 306–308 Pareto diagrams, 603 partial F test, 544 percentile/percentile rank computation, 36 pie chart, 37 Poisson distribution, 125–126 population mean differences, 312, 314 population mean estimates, optimizing of, 245 population proportion, 237, 277 population proportion estimates, optimizing of, 247 population variances, 242, 278–279 power curve, 292, 296 problem solving with, 167–169 random variables, 109–110 881 www.downloadslide.com 882 Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition Back Matter © The McGraw−Hill Companies, 2009 Index Index randomized block design ANOVA, 396–397 residuals, histogram of, 449 runs test, 629–630 sample size, 290, 294 sampling distribution of sample mean, 209 sampling distribution of sample proportion, 210 scatter plot, 38 sign test, 623 simple regression, 421–422, 459 single-factor ANOVA, 377 Solver, 247, 459 Spearman’s rank correlation coefficient, 659–660 t-distribution, 229 t test difference in means, 319–320 testing population mean, 291 time plot, 38 Trend ϩ Season forecasting, 574–576 trend analysis, 563–564 Tukey method, 376 two-way ANOVA, 388 uniform distribution, 130 Wilcoxon signed-rank test, 643 x-bar chart, 606–607 Z-test, 312 Test statistic ANOVA, 351–354, 364 association, large-sample test, 658 chi-square test for independence, 670 Durbin-Watson test, 540 Friedman test, 654 hypothesis test, 266, 272, 276 individual regression slope parameters, 485 Kruskal-Wallis test, 646 linear relationship between X and Y, 435 Mann-Whitney U test, 634 paired-observation t test, 305 population proportions, 325 runs test, 628 sign test, 623 test statistic is t, 272, 313–314 test statistic is Z, 272, 311–312 Tukey pairwise-comparison, 375 two normally distributed populations/ equality of variances, 332 two population means/independent random samples, 310–316 Tests of homogeneity, 675 Theory of probability, 51–52 Thesis, 257 Thesmar, David, 519n Third quartile, “30 rule” (sample size), 194 Thornton, Emily, 285n standard deviations, 24 Three-factor ANOVA, 379, 389–390 Time plots, 29–30, 38 Time series Excel/MINITAB in, 588–591 exponential smoothing methods, 588–582 TINV function, 249 Tiresome Tires I (case), 301 Tiresome Tires II (case), 346 Tolerance limits, 595, 599 Tosi, Henry L., 465n Total deviation of a data point, 369, 439 Total quality management (TQM), 597 Total sum of squares (SST), 440, 475 Transformation of normal random variables, 156–157 of X to Z, 156 inverse transformation of Z to X, 157 summary of, 160 use of, 157–160 Transformations of data, 514, 521 logarithmic transformation, 521–527 to linearize the logistic function, 529 variance-stabilizing transformations, 527–528 Treatment deviation, 357, 359 Treatments, 349 Tree diagram, 71, 79 Trend, 561 Trend analysis, 561–564 curved trends, 562 template for, 563–564 trend ϩ Season forecasting, 574–576 Trial of the Pyx, 595 Tse, Yinman, 577n Tucker, M., 26 Tukey, John W., 29 Tukey pairwise-comparison test, 373–376 conducting the tests, 375 studentized range distribution, 373 template for, 376, 401 test statistic for, 375 Tukey criterion, 373 two-way ANOVA, 388–389 unequal sample sizes/alternative procedures, 376 Turra, Melissa, 652n 25th percentile, standard deviations, 162–163, 702 Two-stage cluster sampling, 188 Two-tailed tests, 267, 269, 271, 435, 622, 628 Two-way ANOVA, 380–391 extension to three factors, 389–391 F ratios and, 384–385 factor B main-effects test, 381 hypothesis tests in, 382–383 Kimball’s inequality, 388 model of, 381–382 one observation per cell, 389–391 803 overall significance level, 388 sums of squares, degrees of freedom, and mean squares, 383–384 template for, 388, 398–399, 402 test for AB interactions, 383 Tukey method for, 388–389 two-way ANOVA table, 384–385 Type I and Type II errors, 289, 310, 350 hypothesis testing, 260–261 instances of, 261 optimal significance level and, 263–264 significance level, 262 U Unbalanced designs, 376 Unbiased estimator, 201 Uncertainty, 196 Uncorrelated variables, 435 Unexplained deviation (error), 439–440 Unexplained variation, 361, 440 Uniform distribution, 129–130 formulas, 129 problem solving with template, 130 Union, 53–54 rule of unions, 67 Union rule, 67 Universal set, 53 Universe, Updegrave, Walter, 323n, 638n Upper control limit (UCL), 599, 606, 608–609, 612, 614 Upper quartile, Useen, Jerry, 45n Utility, 725–728 method of assessing, 727 Utility function, 725–727, 731 Utility scale, 725 V Value at risk, 132–133 Value of information, 728–731 Variability; see Measures of variability Variable selection methods, 545–547 all possible regressions, 545 backward elimination, 545–546 forward selection, 545 stepwise regression, 546 Variance, 15, 102; see also Analysis of variance (ANOVA) defined, 15 of discrete random variable, 104–105 of linear composite, 108 of a linear function of a random variable, 106–107 population variance, 15 quality control, 599 sample variance, 15, 17, 205 www.downloadslide.com Aczel−Sounderpandian: Complete Business Statistics, Seventh Edition Back Matter 804 Index Variance inflation factor (VIF), 535 Variance-stabilizing transformations, 527–528 Vella, Matt, 734n Venn diagram, 53–54 Vigneron, Olivier, 481n Vining, G G., 502n Virtual reality, 30 Volatility, 18, 658n W Wachter, Jessica A., 465n Wagner, Joachim, 438n Wain, Daniel, 604n Wald-Wolfowitz test, 630–631 Wallendorf, Melanie, 437n, 442n Wang, Jeff, 437n, 442n Weak test, 631, 678 © The McGraw−Hill Companies, 2009 Index Weighted average, 102 Weighted least squares (WLS), 494 Weighting factor, 578 Weintraub, Arlene, 281n Weisberg, Sanford, 514n Whiskers, 32 Wilcoxon rank sum test, 633 Wilcoxon signed-rank test, 639–643 decision rule, 640 large-sample version, 640 paired-observations two-sample test, 639–640 template for, 643 test for mean/median of single population, 642 Within-treatment deviation, 360 Wolff, Edward N., 422n Wongsunwai, Wan, 555n Wyer, Robrt S., Jr., 370n X x-bar chart, 604–607 template for, 606–607 x chart, 615 Xia, Yihong, 443n Y Yates correction, 672 Z z distribution, 232, 315 z standard deviations, 163 Z test statistic, 272, 311–312 z value, 163 Zero skewness, 22 Zheng, Lu, 371n ZTEST function, 298 883 www.downloadslide.com ... 19 20 21 22 23 24 25 Quality Mkt Share X Y 121 1 18 02 1345 24 05 1 422 20 05 1687 25 11 1849 23 32 2 026 23 05 21 33 3016 22 53 3385 24 00 3090 24 68 3694 26 99 3371 28 06 3998 30 82 3555 320 9 46 92 3466 424 4... 5,784, 025 3 ,23 4, 725 1, 422 2, 005 2, 022 ,084 4, 020 , 025 2, 851,110 1,687 2, 511 2, 845,969 6,305, 121 4 ,23 6,057 1,849 2, 3 32 3,418,801 5,438 ,22 4 4,311,868 2, 026 2, 305 4,104,676 5,313, 025 4,669,930 2, 133 3,016... 3,8 52 4,801 14,837,904 23 ,049,601 18,493,4 52 4,033 5,147 16 ,26 5,089 26 ,491,609 20 ,757,851 4 ,26 7 5,738 18 ,20 7 ,28 9 32, 924 ,644 24 ,484,046 4,498 6, 420 20 ,23 2,004 41 ,21 6,400 28 ,877,160 4,533 6,059 20 ,548,089