Basic business statistics concepts and applcations 5th by berenson

Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e 5TH EDITION Basic Business Statistics Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e This page is intentionally left blank 5TH EDITION Basic Business Statistics Concepts and applications Berenson Levine Szabat O’Brien Jayne Watson Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019 Pearson Australia 707 Collins Street Melbourne VIC 3008 www.pearson.com.au Authorised adaptation from the United States edition entitled Basic Business Statistics, 13th edition, ISBN 0321870026 by Berenson, Mark L., Levine, David M., Szabat, Kathryn A., published by Pearson Education, Inc., Copyright © 2015 Fifth adaptation edition published by Pearson Australia Group Pty Ltd, Copyright © 2019 The Copyright Act 1968 of Australia allows a maximum of one chapter or 10% of this book, whichever is the greater, to be copied by any educational institution for its educational purposes provided that that educational institution (or the body that administers it) has given a remuneration notice to Copyright Agency Limited (CAL) under the Act For details of the CAL licence for educational institutions contact: Copyright Agency Limited, telephone: (02) 9394 7600, email: info@copyright.com.au All rights reserved Except under the conditions described in the Copyright Act 1968 of Australia and subsequent amendments, no part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner Portfolio Manager: Rebecca Pedley Development Editor: Anna Carter Project Managers: Anubhuti Harsh and Keely Smith Production Manager: Julie Ganner Product Manager: Sachin Dua Content Developer: Victoria Kerr Rights and Permissions Team Leader: Lisa Woodland Lead Editor/Copy Editor: Julie Ganner Proofreader: Katy McDevitt Indexer: Garry Cousins Cover and internal design by Natalie Bowra Cover photograph â kireewong foto/Shutterstock Typeset by iEnergizer Aptarađ, Ltd Printed in Malaysia ISBN 9781488617249 23 22 21 20 19 Pearson Australia Group Pty Ltd   ABN 40 004 245 943 Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e brief contents Preface x Acknowledgements xi How to use this book xii About the authors PART PRESENTING AND DESCRIBING INFORMATION Defining and collecting data Organising and visualising data Numerical descriptive measures PART Basic probability Some important discrete probability distributions The normal distribution and other continuous distributions Sampling distributions 147 180 212 248 DRAWING CONCLUSIONS ABOUT POPULATIONS BASED ONLY ON SAMPLE INFORMATION Confidence interval estimation Fundamentals of hypothesis testing: One-sample tests 10 Hypothesis testing: Two-sample tests 11 Analysis of variance PART 4 37 91 MEASURING UNCERTAINTY PART xvii 279 315 358 401 DETERMINING CAUSE AND MAKING RELIABLE FORECASTS 12 Simple linear regression 13 Introduction to multiple regression 14 Time-series forecasting and index numbers 15 Chi-square tests 455 504 544 607 ONLINE CHAPTERS PART FURTHER TOPICS IN STATS 16 Multiple regression model building 17 Decision making 18 Statistical applications in quality management 19 Further non-parametric tests 20 Business analytics 21 Data analysis: The big picture 650 680 704 740 770 794 Appendices A to F A-1 Glossary G-1 Index I-1 Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e vi detailed contents Preface Acknowledgements How to use this book About the authors x xi xii xvii 3.3 3.4 Calculating numerical descriptive measures from a frequency distribution 118 Five-number summary and box-and-whisker plots 120 3.5 Covariance and the coefficient of correlation 123 PRESENTING AND DESCRIBING INFORMATION 3.6 Pitfalls in numerical descriptive measures and ethical issues Defining and collecting data Summary 130 Key formulas 130 Key terms 132 Chapter review problems 132 Continuing cases 134 Chapter 3  Excel Guide 135 PART 1.1 Basic concepts of data and statistics 1.2 Types of variables 1.3 Collecting data 13 1.4 Types of survey sampling methods 17 1.5 Evaluating survey worthiness 22 1.6 The growth of statistics and information technology 26 Summary 27 Key terms 27 References 27 Chapter review problems 28 Continuing cases 29 Chapter 1  Excel Guide 29 Organising and visualising data 37 2.1 Organising and visualising categorical data 38 2.2 Organising numerical data 43 2.3 Summarising and visualising numerical data 46 2.4 Organising and visualising two categorical variables 55 2.5 Visualising two numerical variables 59 2.6 Business analytics applications – descriptive analytics 62 Misusing graphs and ethical issues 69 2.7 Summary 73 Key terms 73 References 73 Chapter review problems 74 Continuing cases 76 Chapter 2  Excel Guide 77 Numerical descriptive measures 3.1 3.2 Measures of central tendency, variation and shape Numerical descriptive measures for a population 91 92 113 End of Part problems 129 139 PART MEASURING UNCERTAINTY Basic probability 147 4.1 Basic probability concepts 148 4.2 Conditional probability 156 4.3 Bayes’ theorem 163 4.4 Counting rules 168 4.5 Ethical issues and probability 172 Summary 173 Key formulas 173 Key terms 173 Chapter review problems 174 Continuing cases 177 Chapter 4  Excel Guide 178 Some important discrete probability distributions 180 Probability distribution for a discrete random variable 181 5.2 Covariance and its application in finance 185 5.3 Binomial distribution 189 5.4 Poisson distribution 196 5.5 Hypergeometric distribution 200 5.1 Summary 204 Key formulas 204 Key terms 205 Chapter review problems 205 Chapter 5  Excel Guide 208 Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e DETAILED CONTENTS The normal distribution and other continuous distributions 212 6.1 Continuous probability distributions 213 6.2 The normal distribution 214 6.3 Evaluating normality 229 6.4 The uniform distribution 233 6.5 The exponential distribution 235 6.6 The normal approximation to the binomial distribution 238 Summary 242 Key formulas 242 Key terms 242 Chapter review problems 243 Continuing cases 244 Chapter 6  Excel Guide 246 Sampling distributions 248 7.1 Sampling distributions 249 7.2 Sampling distribution of the mean 249 7.3 Sampling distribution of the proportion 259 Summary 262 Key formulas 263 Key terms 263 References 263 Chapter review problems 263 Continuing cases 265 Chapter 7  Excel Guide 265 End of Part problems 267 PART DRAWING CONCLUSIONS ABOUT POPULATIONS BASED ONLY ON SAMPLE INFORMATION Confidence interval estimation 279 Confidence interval estimation for the mean (σ known) 280 Confidence interval estimation for the mean (σ unknown) 285 Confidence interval estimation for the proportion 291 8.4 Determining sample size 294 8.5 Applications of confidence interval estimation in auditing 300 More on confidence interval estimation and ethical issues 307 8.1 8.2 8.3 8.6 Summary 308 Key formulas 308 Key terms 308 References 309 Chapter review problems 309 Continuing cases 313 Chapter 8  Excel Guide 313 Fundamentals of hypothesis testing: One-sample tests 315 9.1 Hypothesis-testing methodology 316 9.2 Z test of hypothesis for the mean (σ known) 322 9.3 One-tail tests 9.4 t test of hypothesis for the mean (σ unknown) 334 9.5 Z test of hypothesis for the proportion 340 9.6 The power of a test 344 9.7 Potential hypothesis-testing pitfalls and ethical issues 349 329 Summary 352 Key formulas 353 Key terms 353 References 353 Chapter review problems 354 Continuing cases 356 Chapter 9  Excel Guide 356 10 Hypothesis testing: Two-sample tests 358 10.1 Comparing the means of two independent populations 359 10.2 Comparing the means of two related populations 371 10.3 10.4 F test for the difference between two variances 378 Comparing two population proportions 384 Summary 389 Key formulas 391 Key terms 392 References 392 Chapter review problems 392 Continuing cases 395 Chapter 10  Excel Guide 396 11 Analysis of variance 401 The completely randomised design: One-way analysis of variance 402 11.2 The randomised block design 415 11.3 The factorial design: Two-way analysis of variance 425 11.1 Summary 438 Key formulas 439 Key terms 440 References 440 Chapter review problems 441 Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e vii viii DETAILED CONTENTS Continuing cases Chapter 11  Excel Guide 443 444 End of Part problems 448 PART DETERMINING CAUSE AND MAKING RELIABLE FORECASTS 12 Simple linear regression 455 14 Time-series forecasting and index numbers 544 14.1 The importance of business forecasting 545 14.2 Component factors of the classical multiplicative time-series model 546 14.3 Smoothing the annual time series 547 14.4 Least-squares trend fitting and forecasting 555 14.5 The Holt–Winters method for trend fitting and forecasting 567 Autoregressive modelling for trend fitting and forecasting 570 12.1 Types of regression models 12.2 Determining the simple linear regression equation 458 14.6 12.3 Measures of variation 467 14.7 Choosing an appropriate forecasting model 579 12.4 Assumptions 473 14.8 Time-series forecasting of seasonal data 584 12.5 Residual analysis 14.9 Index numbers 591 12.6 Measuring autocorrelation: The Durbin–Watson statistic 14.10 Pitfalls in time-series forecasting 599 477 Inferences about the slope and correlation coefficient 482 12.7 456 473 12.8 Estimation of mean values and prediction of individual values 489 12.9 Pitfalls in regression and ethical issues 493 Summary 496 Key formulas 497 Key terms 498 References 498 Chapter review problems 498 Continuing cases 501 Chapter 12  Excel Guide 502 13 Introduction to multiple regression Chi-square test for differences between more than two proportions 615 15.3 Chi-square test of independence 622 504 15.4 Chi-square goodness-of-fit tests 627 15.5 Chi-square test for a variance or standard deviation 632 505 13.2 R 2, adjusted R and the overall F test 511 Residual analysis for the multiple regression model 514 Inferences concerning the population regression coefficients 516 Testing portions of the multiple regression model 520 Using dummy variables and interaction terms in regression models 525 13.5 13.6 13.7 607 608 Developing the multiple regression model 13.4 15 Chi-square tests Chi-square test for the difference between two proportions (independent samples) 13.1 13.3 Summary 600 Key formulas 600 Key terms 601 References 602 Chapter review problems 602 Chapter 14  Excel Guide 604 Collinearity 535 Summary 536 Key formulas 537 Key terms 537 References 537 Chapter review problems 538 Continuing cases 541 Chapter 13  Excel Guide 541 15.1 15.2 Summary 635 Key formulas 635 Key terms 636 References 636 Chapter review problems 636 Continuing cases 640 Chapter 15  Excel Guide 641 End of Part problems 642 PART (ONLINE) FURTHER TOPICS IN STATS 16 Multiple regression model building 650 16.1 Quadratic regression model 651 16.2 Using transformations in regression models 657 16.3 Influence analysis 660 Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e DETAILED CONTENTS 16.4 Model building 663 16.5 Pitfalls in multiple regression and ethical issues 673 Summary 674 Key formulas 674 Key terms 674 References 676 Chapter review problems 676 Continuing cases 677 Chapter 16  Excel Guide 677 17 Decision making Payoff tables and decision trees 681 17.2 Criteria for decision making 685 17.3 Decision making with sample information 694 17.4 Utility 699 Summary 700 Key formulas 701 Key terms 701 References 701 Chapter review problems 701 Chapter 17  Excel Guide 703 704 18.1 Total quality management 705 18.2 Six Sigma management 707 18.3 The theory of control charts 708 18.4 Control chart for the proportion – The p chart 710 The red bead experiment – Understanding process variability 716 18.5 19.1 19.2 740 McNemar test for the difference between two proportions (related samples) 741 Wilcoxon rank sum test – Non-parametric analysis for two independent populations 744 19.3 Wilcoxon signed ranks test – Nonparametric analysis for two related populations 750 19.4 Kruskal–Wallis rank test – Non-parametric analysis for the one-way anova 755 Friedman rank test – Non-parametric analysis for the randomised block design 758 680 17.1 18 Statistical applications in quality management 19 Further non-parametric tests 19.5 Summary 762 Key formulas 762 Key terms 762 Chapter review problems 763 Continuing cases 765 Chapter 19  Excel Guide 766 20 Business analytics 770 20.1 Predictive analytics 771 20.2 Classification and regression trees 772 20.3 Neural networks 777 20.4 Cluster analysis 781 20.5 Multidimensional scaling 783 Key formulas 786 Key terms 787 References 787 Chapter review problems 787 Chapter 20  Software Guide 788 21 Data analysis: The big picture 794 21.1 Analysing numerical variables 798 Control chart for an area of opportunity – The c chart 718 21.2 Analysing categorical variables 800 18.7 Control charts for the range and the mean 721 21.3 Predictive analytics 801 18.8 Process capability 727 18.6 Summary 733 Key formulas 733 Key terms 734 References 734 Chapter review problems 734 Chapter 18  Excel Guide 736 Chapter review problems 802 End of Part problems 804 Appendices A to F A-1 Glossary G-1 Index I-1 Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e ix www.freebookslides.com G-6 GLOSSARY Paasche price index Uses consumption quantities in the final year to weight price changes measured as an index number paired  Observations that are analysed together on the basis of a common characteristic paired t test for the mean difference in related populations A test for the difference between the means of two populations that have a common characteristic parameter  A numerical measure of some population charac­teristics parsimony  The process of choosing the simplest model in terms of independent variables that still adequately explains the variation in the dependent variable partial correlation  The correlation between two variables after removing the effects of other variables; used to identify spurious correlation and hidden correlation (a correlation masked by the effect of other variables) partial F test  Tests for a significant contribution of an individual independent X variable in multiple regression after all other independent X variables have been included in the regression model, using the F probability distribution payoff table  A table that shows the values associated with every possible event that can occur for each course of action payoffs  Values associated with the outcome of events p chart  A control chart for the proportion of nonconforming items Pearson correlation  The correlation coefficient, also called the linear or product-moment correlation; determines the extent to which values of two variables are ‘proportional’ to each other percentage distribution  A summary table for numerical data; it gives the percentage of data values in each class percentage polygon  A graphical representation of a percentage distribution permutation  An ordered selection of items pie chart  A graphical representation of a summary table for categorical data; each category is represented by a slice of a circle of which the area represents the proportion or percentage share of the category point estimate  A single value, calculated from a sample, that is used to estimate an unknown population parameter Poisson distribution  Discrete probability distribution, where the random variable is the number of events in a given interval pooled-variance t test A test for the difference between two population means which assumes that the unknown population variances are equal population A collection of all members of a group being investigated population mean  A mean calculated from population data population standard deviation  A standard deviation calculated from population data population variance  A variance calculated from population data portfolio  A combined investment in two or more assets portfolio expected return A measure of central tendency; a mean return on investment portfolio risk  A measure of the variation of investment returns post-hoc A comparison where hypotheses are formulated after the data have been inspected power curve  A graph showing the power of the test for various actual values of the population parameter power of a statistical test  The probability that you reject the null hypothesis when it is false and should be rejected prediction interval for an individual response Y  The interval for the prediction of a specific value of Y in regression, given a value of X prediction line  The straight line derived by a regression equation using the method of least squares predictive analytics  A form of business analytics that identifies what is likely to occur in the (near) future and finds relationships in data that may not be readily apparent using descriptive analytics prescriptive analytics A form of business analytics that investigates what should occur and prescribes the best course of action for the future price index  A measure of the average price of a group of goods relative to a base year primary source Provides information collected by the data analyser principle of parsimony  The principle that the simplest of two competing statistical processes is to be preferred probability  The likelihood of an event occurring probability distribution for a discrete random variable The values of a discrete random variable with the corresponding probability of occurrence probability sample  A sample where selection is based on known probabilities process  The value-added transformation of inputs to outputs process capability  The ability of a process to consistently meet specified customer expectations processing elements  The hidden layer in multilayer perceptrons (MLPs) pth-order autocorrelation  The correlation between values in a time series that are p periods apart pth-order autoregressive model  A regression model to measure autocorrelation p order apart in a time series p-value  The probability of getting a test statistic more extreme than the sample result if the null hypothesis is true quadratic regression model A multiple regression model with two independent variables, where the second independent variable is the square of the first independent variable quadratic trend model A non-linear forecast model where the second independent variable is the square of the first independent time-series variable qualitative forecasting methods Methods that are primarily based on the subjective opinion of the forecaster rather than the analysis of numerical data quantile–quantile plot  A normal probability plot quantitative forecasting methods  Methods that use time-series data in a mathematical process to forecast future values of the series quartiles  Measures of relative standing that partition a data set into quarters R chart  A control chart for the range random error  An error that results from unpredictable variations random experiment  A precisely described scenario that leads to an outcome that cannot be predicted with certainty randomisation  A process used in an experiment to ensure selection bias is avoided randomised block design An experimental technique where data in groups are divided into fairly homogeneous subgroups called blocks to remove variability from random error Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e www.freebookslides.com GLOSSARY G-7 randomness and independence Assumptions necessary in ANOVA to avoid bias range A distance measure of variation; the difference between maximum and minimum data values ratio scale A ranking where the differences between measurements involve a true zero point recoded variable  A variable that has been assigned new values that replace the original ones rectangular distribution A continuous probability distribution where the values of the random variable have the same probability; also called the ‘uniform distribution’ region of non-rejection  The range of values of the test statistic where the null hypothesis cannot be rejected region of rejection  The range of values of the test statistic where the null hypothesis is rejected; it is also called the ‘critical region’ regression analysis A method for predicting the values of a numerical variable based upon the values of one or more other variables regression coefficients  The calculated parameters in regression that specify the interval and slope of the linear line defining the relationship between the independent and dependent variables regression sum of squares (SSR) The degree of variation between X and Y variables that is explained by the defined regression relationship between the two variables Specifically, the degree of variation in the Y variable that is accounted for by variation in the X variable(s) relative frequency distribution  A summary table for numerical data which gives the proportion of data values in each class relevant range  The range of values of the explanatory variable, which are themselves the only values relevant to predicting any value in regression repeated measurements Data collected from the same set of persons or items at different times replicates  Sample sizes for particular combinations of two factors in two-way ANOVA residual Difference between the observed values and the corresponding values that are predicted by the regression model; they represent the variance that is not explained by the model residual analysis A graphical evaluation of the residuals from regression to test for violations of the assumptions of regression resistant measures Summary measures not influenced by extreme values response variable  A dependent variable return-to-risk ratio (RTRR)  The expected monetary value of an action divided by its standard deviation risk-averter’s curve A utility curve that increases rapidly then levels off as dollar amounts increase risk of Type II error (b)  The chance that the null hypothesis will not be rejected when it is incorrect risk-neutral curve  A utility curve where each additional dollar of profit has the same value risk-seeker’s curve  A utility curve that increases more rapidly as dollar amounts increase robust A test or procedure that is not seriously affected by the breakdown of assumptions sample  The portion of the population selected for analysis sample coefficient of correlation A coefficient of correlation calculated from sample data sample covariance  A covariance calculated from sample data sample mean  A mean calculated from sample data sample proportion  The number of items that have some characteristic of interest divided by the size of the sample sample space A collection of all simple events of a random experiment sample standard deviation A standard deviation calculated from sample data sample variance  A variance calculated from sample data sampling distribution The probability distribution of a given sample statistic with repeated sampling of the population sampling distribution of the mean  The distribution of all possible sample means from a given population sampling distribution of the proportion  The distribution of all possible sample proportions from samples of a certain size sampling error  The difference in results for different samples of the same size sampling with replacement  An item in the frame can be selected more than once sampling without replacement  Each item in the frame can be selected only once scatter diagram A graphical representation of the relationship between two numerical variables; plotted points represent the given values of the independent variable and corresponding dependent variable seasonal component  A factor that measures the regular seasonal change in a time series second-order autocorrelation Indicates there is a correlation between values two periods apart in a time series second-order autoregressive model  A regression model to measure second-order autocorrelation in a time series second quartile  Usually called the median; the middle value in an array that 50% of data values are smaller than, or equal to secondary source  Provides data collected by another person or organisation separate-variance t test A test for the difference between two population means, used when the unknown population variances cannot be assumed to be equal shape  The pattern of the distribution of data values Shewhart–Deming cycle An improvement process used by TQM: ‘plan, do, study, act’ side-by-side bar chart A graphical representation of a crossclassification table simple event  A single outcome of a random experiment simple linear regression A regression method using a single independent variable to predict values of the numerical dependent variable simple price index A percentage measure of the change in the price of a single item between two time periods simple random sample  A sample where each item in the frame has an equal chance of being selected single linkage A measure of distance that bases the distance between clusters on the minimum distance between objects in one cluster and another cluster Six Sigma management An approach to process improvement with an emphasis on accountability and bottom-line results Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e www.freebookslides.com G-8 GLOSSARY skewed  Non-symmetrical distribution; where the distribution of data values above and below the mean differ sparklines  A descriptive analytics method that summarises timeseries data as small, compact graphs designed to appear as part of a table special (or assignable) causes of variation  Large fluctuations or patterns in data that are not inherent to a process; these fluctuations reflect changes in the process specification limits  Technical requirements based on customers’ needs and expectations spread (dispersion)  The amount of scattering of data values square-root transformation  Uses the square-root of the sample data to overcome breaches of the homoscedasticity or linearity assumptions in regression standard deviation A measure of variation based on squared deviations from the mean; closely related to the variance standard deviation of a discrete random variable  A measure of variation, based on squared deviations from the mean; closely related to the variance standard deviation of the sum of two random variables A measure of variation; closely related to the variance standard error  The square root of the expected squared difference between the random variable and its expected value standard error of the estimate The standard deviation of the Y predicted values in a regression around the line of best fit standard error of the mean Reflects how much the sample mean varies from its average value in repeated experiments standard error of the proportion  The standard deviation of the sample proportion for repeated samples standardised normal random variable  A normal random variable with a mean of and a standard deviation of state of statistical control  A process that is in control statistic A numerical measure that describes a characteristic of a sample statistical independence The occurrence of an event does not affect the occurrence of a second event statistical packages Computer programs designed to perform statistical analysis statistics  A branch of mathematics concerned with the collection and analysis of data stem-and-leaf display A graphical representation of numerical data that partitions each data value into a stem portion and a leaf portion stepwise regression A model-building regression technique to find subsets of independent variables that most adequately predict a dependent variable given the specified criteria for adequacy of model fit strata  Subpopulations composed of items with similar characteristics in a stratified sampling design stratified sample  Items randomly selected from each of several populations or strata stress statistic A goodness-of-fit statistic used in multidimensional scaling structured data  Data that follow an organised pattern Studentised deleted residual A statistical method of residual analysis using the t probability distribution that identifies individual cases in the sample data of a multiple regression that have high individual influence on the regression equation Studentised range distribution  A probability distribution used for testing all differences between pairs of means Student’s t distribution A continuous probability distribution whose shape depends on the number of degrees of freedom subgroup  A sample used in a control chart subjective probability  The probability that reflects an individual’s belief that an event occurs sum of squares (SS)  The sum of the squared deviations sum of squares between blocks (SSBL)  That part of the withingroup variation that is due to differences between the blocks sum of squares between groups (SSB)  That part of total variation that is due to differences between groups sum of squares due to factor A (SSA)  Variation due to factor A in two-way ANOVA sum of squares due to factor B (SSBB)  Variation due to factor B in two-way ANOVA sum of squares due to interaction (SSAB) The interacting effect of specific combinations of factor A and factor B sum of squares error (SSE) (or error sum of squares)  The sum of squared differences between the values in each cell and the corresponding mean of that cell sum of squares total (SST) (or total sum of squares)  The total variation; the sum of squared differences between each value and the grand mean sum of squares within groups (SSW)  The sum of squared differences between each value and the mean of its own group summary table  A table that summarises categorical or numerical data; it gives the frequency, proportion or percentage of data values in each category or class symmetrical Where the distribution of data values above and below the mean are identical systematic sample  A method that involves selecting the first element randomly then choosing every kth element thereafter table of random numbers A table showing a list of numbers generated in a random sequence tampering  Over-adjustment that increases variation in a process test of independence  Tests for independence between the rows and columns of a contingency table test statistic A value derived from sample data that is used to determine whether the null hypothesis should be rejected or not third (upper) quartile The value that 75% of data values are smaller than or equal to time series A sequence of measurements taken at successive points in time time-series forecasting methods Statistical methods for forecasting future values of a variable based entirely on the past values of that variable time-series plot A graphical representation of the value of a numerical variable over time total amount  The sum of values total quality management (TQM) An approach to quality improvement that emphasises continuous improvement and the total system total sum of squares (SST) (or sum of squares total)  The total variation total variation  The sum of the squared differences between each individual value and the grand mean Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e www.freebookslides.com GLOSSARY G-9 training data  A set of data used by neural networks to uncover a model that by some criterion best describes the patterns and relationships in the data transformation formula A Z-score formula used to convert any normal random variable to the standardised normal random variable treatment effect  A variation due to group membership treemaps  A descriptive analytics method that helps visualise two variables, one of which must be categorical trend component An overall long-term upward or downward movement in the values of a time series t test for the correlation coefficient  A hypothesis test for the statistical significance of the correlation coefficient in regression using the t probability distribution t test for the slope A hypothesis test for the statistical significance of the regression slope b using the t probability distribution t test of hypothesis for the mean A test about the population mean that uses a t distribution Tukey–Kramer multiple comparison procedure A method of determining which of the group means are significantly ­different Tukey procedure A method of making pairwise comparisons between means two-factor factorial design  Analysis of variance where two factors are simultaneously evaluated two-tail test A hypothesis test where the rejection region is ­divided into the two tails of the probability distribution two-way ANOVA  An analysis of variance where two factors are simultaneously evaluated Type I error  The rejection of a null hypothesis that is true and should not be rejected Type II error  The non-rejection of a null hypothesis that is false and should be rejected unbiased  If the average of all possible sample means equals the population mean then the sample mean is unbiased unexplained variation  The error sum of squares uniform distribution A continuous probability distribution in which the values of the random variable have the same probability; also called the ‘rectangular distribution’ unstructured data  Data that have no repeated pattern unweighted aggregate price index  A price index for a group of items where each item has an equal weight upper control limit (UCL)  The upper limit for a control chart, typically three standard deviations above the process mean upper specification limit (USL)  The largest value a CTQ can have to meet customer expectations utility  A measure of the desirability of different outcomes for an individual decision maker variables  Characteristics or attributes that can be expected to differ from one individual to another variables control charts  Control charts for numerical ­variables variance A measure of variation based on squared deviations from the mean; closely related to the standard deviation variance inflationary factor (VIF) A factor that measures the impact of collinearity among the Xs in a regression model by stating the degree to which collinearity among the predictors reduces the precision of an estimate variance of a discrete random variable  A measure of variation, based on squared deviations from the mean; closely related to the standard deviation variance of the sum of two random variables A measure of variation; closely related to the standard deviation variation  The spread, scattering or dispersion of data values Venn diagram  The graphical representation of a sample space; joint events shown as ‘unions’ and ‘intersections’ of circles representing simple events Ward’s minimum variance method  A measure of distance that bases the distance between clusters on the sum of squares over all variables between objects in one cluster and another cluster weighted aggregate price index A price index for a group of items where each item has a different weight based on volume of consumption Wilcoxon rank sum test A non-parametric test for testing the difference between two medians from independent ­samples Wilcoxon signed ranks test  A non-parametric test for testing the mean difference for paired samples within-group variation  That part of total variation due to differences within individual groups – X chart  A control chart for the process mean Y intercept  Represents the mean value of Y when X equals zero in regression Z scores  Measures of relative standing; number of standard deviations given data values are from the mean Z test for the difference between two means  A test statistic used in hypothesis tests about the difference between means of two populations Z test for the difference between two proportions  A test statistic used in hypothesis tests about the difference between the proportions of two populations Z test for the proportion A test statistic used for a test of the population proportion Z test of hypothesis for the mean A test about the population mean which uses the standard normal distribution Z test statistic  A test statistic calculated by converting a sample statistic to a standard normal score Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e www.freebookslides.com This page is intentionally left blank www.freebookslides.com index Page numbers in bold indicate definitions of key terms Page numbers in italics indicate figures tables  608–9, 611 3 tables  616 3 tables  625 a priori classical probability  148, 148–9 ABS (Australian Bureau of Statistics)  6, 8, 14, 24 accounting 8 adjusted R2  511, 537, 542–3 aggregate price indices  591, 593–4 All Australia Index  596 All Industries Index  597 alternative hypotheses (H1) 316–17, 317, 323–4, 332 analysis of variance (ANOVA), defined  402 see also one-way analysis of variance; randomised block design; two-way analysis of variance annual time-series data  545 ANOVA summary tables  405, 406–8, 408, 419, 430 Anscombe’s quartet  494 arithmetic mean  92, 92–3 artificial data  494 assumptions of regression (LINE)  473 ASX 200 Index  596–7 auditing  300, 300–7 Australian Bureau of Statistics (ABS)  6, 8, 14, 24 Australian Securities Exchange (ASX)  597 autocorrelation defined  477 first-order  570 measuring with Durbin–Watson statistic  477–80, 480, 503 pth-order  570 regression analysis  475, 477–80, 478–80 second-order  570 autoregressive modelling  570, 570–8, 573, 575–8, 600–1, 605–6 averages  see moving averages bar charts  39, 39–40, 39–40, 79 base period  591 Bayes’ theorem  163, 163–6, 168–9, 173, 178 bell-shaped distribution  115, 122, 122, 213, 214 between-block variation  416, 416, 417, 417–18 between-group variation  402, 403, 416, 416, 417–18, 439 bias 25 big data  14, 14–15 bin ranges  83 binomial distribution binomial probabilities  191–5, 193–4 defined  189 example 190 formula  191, 204 mean  194, 205 normal approximation to  238–41, 240, 242 properties 189 standard deviation  194, 205 using statistical software  193, 193–4 binomial probabilities  191–5, 193–4 block effects  416, 416–22, 421 blocks  416 see also randomised block design box-and-whisker plots confidence interval estimation  289 defined  121 examples 121–2, 121–2 one-sample tests  338, 350 two-sample tests  364, 375 using Excel  137–8, 138 boxplots 121 brainstorming 14 bullet graphs  64, 64–5, 65, 66, 89–90 business analytics  62–7, 63 business forecasting  545 CAI (Computer Assisted Interview)   24 call monitoring  368 car exports  505 categorical data, tables and charts for  38–42, 73, 77–9 categorical variables  9–11, 10, 10, 55–7, 86–7, 527–8 causal forecasting methods  545 cell means plots  432–4, 432–4, 447 censuses  8, 26 Central Limit Theorem  214, 256, 256–8, 257, 266, 280, 322, 334, 337 central tendency  92, 92–9, 135–6 certain events  148 chartjunk  65 charts bar charts  39, 39–40, 39–40, 79 bullet graphs  64, 64–5, 65 for categorical data  38–42, 39–41 choosing an appropriate chart  73 misusing graphs  69–71, 69–71 for numerical data  46–53 pie charts  40, 40–2, 41, 79 side-by-side bar charts  56, 56–7, 56–7 using statistical software  79 see also scatter diagrams; time-series plots Chebyshev rule  116, 116–17, 137 chi-square analysis chi-square (x2) distribution  610 x2 test statistic  609–13, 612, 615–18, 622–33, 641 goodness-of-fit tests  627, 627–31, 635 key formulas  635 Marascuilo procedure  619, 619–20, 620, 635 test for differences between more than two proportions 615–20, 616, 618, 620, 635, 641 test for differences between two proportions 608–13, 610, 612–13, 635, 641 test for standard deviation  632–3, 632–3, 635 test for the variance  632–3, 632–3, 635 test of independence  622, 622, 622–6, 625, 641 using statistical software  612–13, 618, 620, 625, 633, 641 chi-square (x2) distribution  610 chunk samples  17 class boundaries  47 class mid-point  47, 83 class width  46, 46–7 classical multiplicative time-series model  546, 546–7, 585, 600 classical parametric procedures  337 classical statistical inference  214 cluster samples  17, 21 clusters  21 coefficient of correlation  125, 125–8, 138, 486, 497, 503 coefficient of determination  469, 469–71, 470, 497 coefficient of multiple determination  511, 511–12, 537, 542–3 coefficient of partial determination  523, 523–4, 537 coefficient of variation  105, 105–6, 131, 136–7 collectively exhaustive events  16, 47, 153, 215 collinearity  535, 535–6 combinations  170, 170–1, 173, 179, 190–1, 204 complement  150 completely randomised designs  402, 403, 416, 444–5 Computer Assisted Interview (CAI) techniques 24 computer technology  26 conditional probability  156, 156–61, 164, 173 confidence coefficient (1 a)  319 confidence interval estimate, defined  280, 485 confidence interval estimation applications in auditing  300–7 compared with prediction interval  492, 492 difference between the means of two independent populations  364–5, 391 difference between the means of two related populations  377, 391, 397 difference between two proportions  388, 391, 400 ethical issues  307 and hypothesis testing  327–8 for the mean (s known)  280–4, 281, 283, 308, 313 for the mean (s unknown)  285–6, 285–90, 288–9, 308, 313 for the mean difference  377 for the mean of Y  489–91, 497 of the mean response  508, 508 one-sided  304, 304–5 for the population total  300–2, 314 for the proportion  291–3, 292, 305, 308, 314 of the slope  485, 497, 537 for total difference  314 using statistical software  288, 289 value of a population slope  518–19 see also difference estimation; sample size determination Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e www.freebookslides.com I-2 INDEX confidence interval statements  287–8, 288 confidence level  319 consent, in research  350 Consumer Price Index (CPI)  595, 596 contingency tables tables  608–9, 611 3 tables  616 3 tables  625 chi-square analysis  608–9, 615 defined  55, 608 examples of  55–7 probability  150 using statistical software  86–7, 625 continuity corrections  238–9 continuous numerical variables  181 continuous probability density function  213, 213–14 continuous probability distributions  146, 213–14, 405 continuous random variables  213–14, 238–9 continuous variables  10 convenience sampling  17, 17 correlation coefficient  125, 125–8, 138, 486, 497, 503 counting rules  168–71, 173, 178–9 covariance  123, 123–5, 138, 185, 185–8, 204, 209 coverage errors  23, 25 CPI (Consumer Price Index)  595, 596 critical range factor A  436, 440 factor B  436, 440 for Marascuilo procedure  619 randomised block design  422–3, 439 for Tukey–Kramer procedure  409–10, 439 for Tukey procedure  438 critical region  318 critical value approach to hypothesis testing  322–5, 323 to one-tail tests  329–30, 330 t test for the mean (s unknown)  334–6, 335 Z test for the proportion  341–2, 341–2 critical values  283, 286, 318, 319, 335, 335, 380–2, 381–2, 391 CRM (customer-relationship management system) 26 cross-classification (contingency) tables  55, 150, 608, 608–9 cross-product term  528 cumulative percentage distributions  49, 49–50, 82, 85–6 cumulative percentage polygons (ogives)  52, 52–3, 53 cumulative standardised normal distribution  217, 217–18, 219, 223 curvilinear relationship  457, 457–8 customer-relationship management system (CRM) 26 cyclical component  546, 546–7 dashboards 63–6, 64, 64 data analysing  129, 350–1 big data  14, 14–15 categorical  9–11, 38–42 cleaning  15–16, 350–1 collecting  13–16, 350 defined  discarding 350–1 formatting 15 independence of  420 interpreting 129 measuring 10–11 numerical  9–11, 43–53 randomness 350 sources of  13–14 stacked and unstacked data  79 structured  15 unstructured  15 Data Analysis Toolpak  see Microsoft Excel data discovery  66 data mining  26 data point  data snooping  350 Dax 30 Index  597 decision making, in hypothesis testing  320 decision trees  158, 158–9, 158–9, 165–6 deductive reasoning  281 degrees of freedom  285, 285–7, 286, 366, 391, 404 Delphi technique  14 dependent variables  456, 507–8, 508 descriptive analytics  62–7, 63, 88–90 descriptive statistics  8, 55, 109 see also numerical descriptive measures difference estimation  302, 302–4 diffusion indices  545 directional tests  330 discrete random variables  181–4, 185–7, 208 discrete variables  10 dispersion (spread)  99 distribution bell-shaped  115, 122, 122, 214 exponential 213, 214, 235, 235–7, 236, 242, 247, 247, 257, 257–8 hypergeometric distribution  200, 200–2 probability distribution for a discrete random variable  181, 181–4, 182, 208 shape  107, 107–9 skewed distribution  107, 107, 107–8, 109, 110, 120, 137 symmetrical  107, 107, 107–8, 109, 120 uniform 213, 214, 233, 233–4, 234, 256, 257, 258 see also binomial distribution; chi-square distribution; normal distribution; Poisson distribution; sampling distributions double exponential smoothing  555 Dow Jones Industrial Average  596 drill-down  66 dummy variables  525–31, 526, 527, 529–30, 532, 587 Durbin–Watson statistic  475, 479, 479–80, 480, 497, 503 econometric modelling  545 electronic formats  15 empirical classical probability  149 empirical rule  115, 115–16, 137 encoding  15 equal variance  473, 476, 476 error sum of squares (SSE)  467, 468, 468–9, 497, 581 see also sum of squares error (SSE) errors independence of  473 random error  402 residual 579–80 Type I errors  319, 319–21, 344 Type II errors  319, 319–21, 344, 345–6, 345–6 estimated relative efficiency (RE)  422, 439 ethical issues calculating probabilities  172 confidence interval estimation  307 hypothesis testing  349–51 misuse of graphs  70–1, 70–1 selective use of statistics  129–30 survey errors  25 using numerical descriptive measures  129–30 using regression analysis  493–4, 495, 496 events certain events  148 collectively exhaustive events  16, 47, 153, 215 complement of  150 defined  149 impossible events  148 independent events  159–61 joint events  150 mutually exclusive events  16, 47, 153, 215 rare events  60–1 sample spaces and  150 simple events  149 Excel  see Microsoft Excel exchange rate  505 executive information systems  63 expected frequency  609, 611–13, 612–13, 615–19, 623–8, 630, 635 expected returns  187–8 expected value of a discrete random variable  182, 182–3, 204 of the sum of two random variables  186, 186–7, 204 explained variation  467 explanatory variables  457, 525 exponential distribution  213, 214, 235, 235–7, 236, 242, 247, 247, 257, 257–8 exponential growth, forecasting equations  586, 601 exponential smoothing  551, 551–3, 552, 600, 604 exponential trend model  558, 558–60, 560–1, 581, 582–3, 585–8, 588, 600–1, 605 exponentially weighted moving averages  551 extrapolation (regression analysis)  463, 493 extreme values (outliers)  106 F distribution  378, 380–1, 381, 391, 405 F test for block effects  419–20, 421 for the difference between two variances 378–83, 379, 381–2, 391, 399–400, 399–400 for differences between more than two means 402–8, 403, 405–6, 408 for factor A effect  428, 440 for factor B effect  428, 428–9, 440 for interaction effect  429, 440 one-way ANOVA F test  402–8, 403, 404, 405–6, 408, 439 overall F test  511–12, 512, 513, 537, 542–3 partial F test  520, 520–3, 537 for the slope  484, 484–5, 484–5, 497 Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e www.freebookslides.com INDEX F test statistic  378, 378–80, 391, 419, 439, 512, 522–3 factor A  426–8, 436, 439, 440 factor B  426–8, 436, 439, 440 factorials  169, 173, 179 factors (variables)  402 finance, use of statistics in  8, 187–8, 209 financial indices  596–7 finite population correction factor  201 first differences  561–3, 605 first (lower) quartile  97, 100, 130 first-order autocorrelation  570 first-order autoregressive model  570–1, 571, 575, 577–8, 577–8, 581, 582–3, 600 fitted pth-order autoregressive equation  573, 601 five-number summary  120, 120–1, 137 focus groups  14 forecasting  see time-series forecasting frame  17 frequencies  see expected frequency; observed frequency frequency distributions approximating standard deviation from  131 approximating the mean from  131 constructing 46–8 defined  46 finding numerical descriptive measures from 118–19 relative frequency distributions  48–9 using statistical software  80–4, 81 frequency polygons  83 Friedman rank test  420 gauges  64, 64–6, 65, 88–9 Gaussian distribution  214 general addition rule  154, 154–5, 173 general multiplication rule  160, 160–1, 173 geometric mean  98, 98–9, 130 geometric mean rate of return  98–9, 131 goodness-of-fit tests  627, 627–31, 635 Gosset, William S.  285 grand mean  403 graphs bullet graphs  64, 64–5, 65 misuse of  69–71, 69–71 groups  402 halo effect  25 highest-order autoregressive model  571–3, 575, 601 histograms  50, 50–1, 82–5 Holt–Winters method  567, 567–8, 569, 581, 582–3, 600 homogeneity of variance  411, 412, 445 homoscedasticity  473 households  108, 108–9 Human Development Index  456–64, 460–1, 468, 469, 471, 475–6, 483–6, 484, 489–92 hypergeometric distribution  200, 200–2, 205, 211 hypothesis testing comparing the means of two independent populations 359–68, 361–4, 367, 391, 396–8, 396–8 comparing the means of two related populations 371–7, 374–6, 391, 398–9, 398–9 comparing two population proportions  384–8, 385–6, 391, 400, 400 and confidence interval estimation  327–8 confidence level  319 confirmatory approach  359 critical value approach  322–5, 323, 329–30, 330, 334–6, 335, 341–2, 341–2 decision-making risks  319–21 defined  316 ethical issues  349–51 F test for difference between two variances 378–83, 379, 381–2, 399–400, 399–400 hypothesis-testing methodology  316–21 in multiple regression models  516–19, 517 null and alternative hypotheses  316–17, 323–5, 327, 332, 350 one-sample tests  316–57 p-value approach  325–7, 326, 331–2, 342–3 potential pitfalls  349–51 power of a statistical test  320, 320–1, 344–7, 344–8 regions of rejection and non-rejection  318, 318–19, 323, 324 selecting a test  352, 353 six-step method  323–4 t test of hypothesis for the mean  334, 334–7, 335–8 test statistic  318, 323–4 two-sample tests  359–400 using statistical software  326, 326, 331, 336–7, 336–8, 342, 356–7, 362–3, 367, 374, 376, 381, 386, 396–400, 397–400 Z test of hypothesis for the mean  322, 322–8, 323, 326 Z test of hypothesis for the proportion  340, 340–3, 341 see also chi-square analysis; F test; one-tail tests; t test; two-tail tests; Z test impossible events  148 independence in ANOVA  410, 420 chi-square test of  622, 622, 622–6, 625, 641 of data  420 of errors  473 in regression analysis  475 statistical  159, 159–60 independent events  159–61 independent populations  359–68, 361–4, 367, 378, 391, 396–8, 396–8 independent variables  456, 506–7, 520, 523–4, 528–9, 535–6, 537 index numbers  591, 591–7 inductive reasoning  281 inferential statistics  8, 26, 280–1 information technology  26 informed consent  350 insurance premiums  613 interaction effects  420, 422, 426, 426, 426–35, 430–5, 447 interaction terms  528 interactions (variables)  528, 528–31, 529–30, 532 interpolation (regression analysis)  463 interquartile range  100, 100–1, 105, 131, 136 interval estimates  see confidence interval estimation interval scales  11, 11 I-3 intervals 280 investment services  14 irregular (random) component  546, 546–7 joint events  150 joint probability  152, 152–3 judgment samples  17, 17 kurtosis  109, 137 labour force participation rates, for females  546, 546 lagged predictor variables  545, 605 Laspeyres price index  594, 594–5, 596, 601 leading indicator analysis  545 leading questions  24 least-squares method  459–61, 460, 460–1, 555–63, 557, 581, 606 least-squares trend-fitting and forecasting  555–63, 557, 585–9, 588, 605 level of confidence  282, 282–4 level of significance (a)  319, 323–4, 350, 431 levels (factors)  402 Levene test  411, 445 LINE  473, 474 linear relationship  457, 457–8 linear trend models  555, 555–6, 557, 561–2, 581, 582–3, 600, 605 linearity  473, 474, 475 lotteries 172 lower quartile  97, 100, 130 lower-tail critical values  380–2, 381–2, 391 MAD (mean absolute deviation)  580, 601, 606 main effects  431, 432 management 8 Marascuilo procedure  619, 619–20, 620, 635 margin of error  295 marginal probability  151, 151–2, 173 market research  14 marketing 8 matched observations  371, 373 mathematical models  189 mean arithmetic mean  92, 92–3 of binomial distribution  194, 205 calculation of  92–3, 135 comparing the means of two independent populations 359–68, 361–4, 367, 391, 396–8, 396–8 comparing the means of two related populations 371–7, 374–6, 391, 398–9, 398–9 confidence interval estimation  280–90, 281, 283, 285–6, 288–9, 308, 313, 364–5, 377, 391 defined  92 exponential distribution  236, 242 F test for differences between more than two means 402–8, 403, 405–6, 408 from a frequency distribution  118–19, 131 geometric mean  98, 98–9, 130 grand mean  403 of hypergeometric distribution  201, 205 versus median  110 normal distribution  216, 216, 219 one-tail test of hypothesis for  330, 330, 331–2 Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e www.freebookslides.com I-4 INDEX mean (continued) related populations  371–7, 374–6 sample mean  93, 93–4 sample size determination  294–6, 296, 308, 314 sampling distribution of  249–58, 253, 256, 263 in shape of distribution  107–8 standard error of  251, 251–2, 252, 307 t test of hypothesis for  334, 334–7, 335–8, 353, 356 unbiased property of  249–51 uniform distribution  233, 234, 242 Z test of hypothesis for  322, 322–8, 323, 326, 353, 356 see also population mean mean absolute deviation (MAD)  580, 601, 606 mean difference  302 mean square between (MSB)  404 mean square between A (MSBA)  428 mean square between AB (MSBAB)  428 mean square between B (MSBB)  428 mean square between blocks (MSBL)  418, 418–19 mean square error (MSE)  418, 418–19 mean square total (MST)  404 mean square within (MSW)  404 mean squares  418–19, 439 mean values, estimating  489–92, 503 measurement error  24, 24–5 measurement, scales of  11–12, 11–12 see also numerical descriptive measures median  94, 94–6, 110, 130, 135 Microsoft Excel analysis of variance  408, 412, 430, 433–5, 444–7, 444–7 autoregressive modelling  575–7 bar charts  39–40, 79 basic probabilities  178 basics 30–1 Bayes’ theorem  178 binomial probabilities  193, 193–4, 209–10 box-and-whisker plots  137–8, 138, 289, 338, 375 bullet graphs  89–90 calculating coefficient of correlation  138 calculating covariance  138 calculating mean, median and mode  135, 135 calculating quartiles  136 calculating variation  136–7 Central Limit Theorem  266 chi-square analysis  612–13, 618, 620, 625, 633, 641 coefficient of variation  136–7 collecting data  35 conditional probability  178 confidence interval estimates  288, 289, 292, 313–14, 492 contingency tables  86–7 counting rules  178–9 covariance of a probability distribution  209 creating charts  33 Data Analysis Toolpak  109, 109 defining classes, bins and mid-points  83–4 defining data  35 descriptive measures for a population  137 descriptive statistics  230 determining sample size  296 entering data  31–3, 32 evaluating normality  246, 246–7 exponential distribution  236, 236, 247, 247 F test for difference between two variances  381 frequency distributions  80–2, 81 gauges 88–9 histograms  50, 83–5 hypergeometric distribution  202, 202, 210, 211 hypothesis testing  326, 326, 331, 336–7, 336–8, 342, 356–7, 362–3, 367, 374, 376, 381, 386, 396–400, 396–400 Marascuilo procedure  620 multiple regression  507–8, 514–15, 515–16, 527, 527, 529–30, 532, 541–3, 542 normal distribution  246 normal probabilities  226, 227, 230, 246, 246–7 normal probability plots  232, 338 numerical descriptive measures for a population 137 ogives 85 one-sample t test  336, 336 opening and saving workbooks  31 ordered arrays  80 paired t tests  376 percentage and cumulative percentage polygons 85–6 pie charts  41, 79 Poisson distribution  198, 210 polygons 85 pooled t tests  362–3 printing workbooks  33–5, 34 probability distribution for a discrete variable 208 probability plots  289, 338 problems with early versions of  26 randomised block design  421, 446, 446 relative frequency  82 residual analysis  478–9, 514–15, 515–16 sample size determination  314 sampling distributions  82, 265, 265 scatter diagrams  59, 87, 87–8, 408, 459, 461 separate-variance t test  367 side-by-side bar charts  56, 87 side-by-side charts  87 simple linear regression  460–1, 461–2, 469, 472, 475, 483, 492, 492, 502, 502–3, 521 sparklines 88 stacked and unstacked data  79 standard deviation  136–7 stem-and-leaf displays  80 summary tables  77–8, 77–8 tables and charts  45 time-series forecasting  550, 552, 557–8, 569, 575–7, 582–3, 585, 588, 604, 604–6, 606 time-series plots  60, 88 Tukey–Kramer procedure  410 two-sample tests  338, 396–400, 396–400 types of sampling methods  36 using Excel on a Mac  35 using formulas in worksheets  33 variance 136–7 Z scores  136–7 Z test for difference between two proportions  386 Minitab (software)  26 missing values  16 mode  98, 135 Morningstar 14 moving averages  548, 548–51, 550, 604 MSB (mean square between)  404 MSBA (mean square between A)  428 MSBAB (mean square between AB)  428 MSBB (mean square between B)  428 MSBL (mean square between blocks)  418, 418–19 MSE (mean square error)  418, 418–19 MST (mean square total)  404 MSW (mean square within)  404 multiple comparisons  408, 408–10, 410, 422–3, 435–6, 445 multiple determination, coefficients of  511, 511–12, 537, 542–3 multiple regression models  505–36 coefficients of multiple determination  511, 511–12, 537, 542–3 coefficients of partial determination  523, 523–4, 537 collinearity  535, 535–6 confidence interval estimate for the slope  518–19, 537 defined  505 dummy variables  525–31, 526, 527, 529–30, 532 interactions  528, 528–31, 529–30, 532 interpreting the regression coefficient  505–7 with k independent variables  506, 524, 537 key formulas  537 overall F test  511–12, 512, 513, 537, 542–3 partial F test  520, 520–3 population regression coefficients  516–19, 517, 543 predicting the dependent variable Y 507–8, 508, 542 residual analysis for  514–15, 515–16, 543 testing for significance of overall model  512, 513 testing for the slope  516–18, 517, 537 testing portions of  520–4, 521–2, 543 with two independent variables  506–7, 507, 537 using statistical software  507–8, 527, 527, 529–30, 532, 541–3, 542 multiplication rule for independent events  161, 173 multiplication rules  160–1 multiplicative model  546, 546–7, 585, 600 mutually exclusive events  16, 47, 153, 215 NASDAQ Index  596 National Health Survey (2010–11)  24 negatively skewed distribution  107, 107–8, 120 net regression coefficients  506 Newspoll 12 Nielsen 14 Nikkei Index  597 nominal scales  10, 10, 10–11 non-compliance, rate of  304–5 non-parametric procedures  337, 364, 375 non-probability sampling  17, 17, 17–18, 25 non-response bias  23 non-response errors  23, 25 Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e www.freebookslides.com INDEX normal distribution approximating binomial distribution  238–41, 240, 242 bell-shaped curve of  213, 214 chi-square goodness-of-fit tests for  629–31 constructing normal probability plots  231, 232 cumulative standardised  217, 217–18, 219 defined  214 different normal distributions  216, 216, 219 evaluating normality  227, 229–31, 230, 232, 246, 246–7 example calculations  219–26, 220–2, 224–5 misapplication of in business  227 sampling distribution  256–7, 257 standardised normal distribution  285, 285 theoretical properties  214, 229–31 transformation formula  216, 216–19, 217–19, 224 using statistical software  226, 227, 246–7, 246–7 normal probability density function  215, 215–18, 242 normal probability plots  231, 232, 246, 289, 338 normality  227, 229–31, 230, 232, 246, 246–7, 410, 420, 473, 476 null hypothesis (H0)  316, 316–17, 323–5, 327, 332, 350 numerical data, tables and charts for  9–11, 43–53, 73, 79–86 numerical descriptive measures box-and-whisker plots  121, 121–2, 121–2 coefficient of variation  105, 105–6 ethical issues  129–30 five-number summary  120, 120–1 from a frequency distribution  118–19 measures of central tendency  92–9 objectivity in data analysis  129 for a population  113–17, 137 shape  92, 107, 107–9 variance and standard deviation  101–5 Z scores  106, 106–7 numerical variables  9–11, 10, 10, 59–61, 181 objectivity, in data analysis  129 observation 6 observational studies  14 observed frequency  609, 611, 623, 627–8 observed level of significance (p-value) 325 OECD (Organisation for Economic Co-operation and Development)  458 ogives  52, 52–3, 53, 85 one-factor experiments  402 one-sample tests  316–57 flow chart for selecting  352 one-sample t test  336 potential pitfalls  349–51 power of a statistical test  320, 320–1, 344–7, 344–8 t test of hypothesis for the mean  337 using statistical software  356–7 Z test of hypothesis for the mean  337, 353 Z test of hypothesis for the proportion  340, 340–3, 341, 353 see also hypothesis testing; one-tail tests one-sided confidence interval  304, 304–5 one-tail tests choice of  350 comparing two population proportions  364–5 critical value approach  329–30, 330 defined  330 ethical considerations  350 F test for difference between two variances  382, 382–3 for the mean  330, 330, 331–2 p-value approach  331–2 power of a test  344, 344–5, 347, 347 t test  374 Z test for population mean  344, 344 one-way analysis of variance  402–13 assumptions  402, 410–11 between-group variation  402, 403, 439 calculating mean squares  404, 439 completely randomised design  402–13, 403, 405–6, 408, 410, 412 defined  402 example calculation  412–13 F test for differences between more than two means 402–8, 403, 405–6, 408 F test statistic  404, 404–5, 405, 439 key formulas  439 Levene test  411 summary tables  405, 406–8, 408, 419 total variation  403, 403, 403–4, 439 Tukey–Kramer procedure  408, 408–10, 410, 413, 435, 439, 445 using statistical software  406, 408, 412, 444–5, 445 within-group variation  402, 404, 439 see also randomised block design online surveys, rigging of  24 operational definition  6, 16 opinion polls  307 ordered arrays  43, 43–4, 80 ordinal scales  10–11, 11, 11 Organisation for Economic Co-operation and Development (OECD)  458 outliers  16, 106 overall F test  511–12, 512, 513, 542–3 p-value  325 p-value approach to hypothesis testing  325–7, 326 to one-tail tests  331–2 t test for the mean (s unknown)  336–7 to two-tail tests  325–6, 326 Z test for the proportion  342, 342–3 Paasche price index  595, 595–6, 601 paired observations  371 paired t test  372, 372–6, 374–6, 391, 398–9, 398–9 parameters  8, parametric procedures  337 parsimony  581 partial determination, coefficient of  523, 523–4, 537 partial F test  520, 520–3, 537 partial regression coefficients  506 Pearson, Karl  227 percentage differences  561–3, 605 percentage distributions  48, 48–9, 82 percentage polygons  51, 52, 85–6 perfect negative correlation  125, 125 I-5 perfect positive correlation  125, 125 perishable inventory  63 permutations  170, 173, 179 PHStat  see Microsoft Excel pie charts  40, 40–2, 41, 79 point estimate  280 Poisson distribution calculating probabilities  197–9 chi-square goodness-of-fit tests for  627–9 defined  196 formula 205 properties 196 relation to exponential distribution  235 using statistical software  198, 210 political polls  307 polls  12, 172, 307 polygons 51–3, 52–3, 83, 85–6 pooled-variance t test  360, 360–4, 361–4, 391, 396–7, 396–7 population comparing the means of two independent populations 359–68, 361–4, 367, 391, 396–8, 396–8 comparing the means of two related populations 371–7, 374–6, 391, 397, 398–9, 398–9 comparing two population proportions  384–8, 385–6, 391, 400, 400 defined  estimating total amount  300, 300–2, 314 estimating unknown characteristics  280–2, 281 examples of  8–9 independent populations  359–68, 361–4, 367 numerical descriptive measures for  113–17, 137 related populations  371–7, 374–6 sampling from non-normally distributed populations 256–8, 257 sampling from normally distributed populations 252–6, 253 see also confidence interval estimation; proportions population mean calculation of  114, 137 defined  113 formula  114, 131, 263 power of a statistical test  344–7, 344–8 sampling distributions  250 Z test for  344, 344 population parameters  113, 332 population proportions  259–60, 297–9, 298 population regression coefficients  516–19, 517, 543 population standard deviation  114, 114–15, 131, 137, 250–1, 263, 333, 334 population variance  114, 114–15, 131, 137 portfolio expected return  187, 187–8, 204 portfolio risk  187, 187–8, 204 portfolios  187, 209 positively skewed distribution  107, 107–8, 120 post-hoc comparison  408 poverty, measures of  110 power curve  347, 347 power of a statistical test  320, 320–1, 344–7, 344–8 practical significance  351 Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e www.freebookslides.com I-6 INDEX prediction interval for an individual response Y  491, 491–2, 493, 497, 503, 508, 508 prediction line  459, 461–3, 497 predictions, in regression analysis  462–3, 503 predictive analytics  63 prescriptive analytics  63 price indices  591–7, 601 primary sources, of data  13, 13–14 prior probabilities  163 probability a priori classical probability  148, 148–9 basic concepts  148–55 Bayes’ theorem  163, 163–6, 168–9 conditional probability  156, 156–61, 164, 173 contingency tables  150 continuous probability distributions  146, 213–14 counting rules  168–71, 173, 178–9 defined  148 empirical classical approach  149 ethical issues  172 events 149–50 general addition rule  154, 154–5, 173 impossible events  148 joint probability  152, 152–3 marginal probability  151, 151–2, 173 of occurrence  148, 173 sample space  149 subjective  149 using statistical software  178–9 Venn diagrams  150, 150–1, 151 see also binomial distribution; normal distribution; Poisson distribution probability distribution, for a discrete random variable  181, 181–4, 182, 208 probability samples  17, 18 proportions calculating overall proportions  610, 610–11, 615–16, 616, 635 chi-square test for differences between more than two  615–20, 616, 618, 620, 635, 641 chi-square test for differences between two 608–13, 610, 612–13, 635, 641 comparing two population proportions  384– 7, 385–6, 391, 400, 400 confidence interval estimates for  291–3, 292, 305, 314, 388, 400 population proportions  259–60, 263 sample size determination  297–9, 298, 308, 314 standard error of  307 Z test for the difference between two  384–7, 385–6, 391, 400, 400 Z test of hypothesis for  340, 340–3, 341, 352, 353, 357 pth-order autocorrelation  570 pth-order autoregressive forecasting equation  573–4, 601 pth-order autoregressive model  570–1, 571, 575, 581, 601 quadratic trend model  557, 557–8, 558–9, 562, 581, 582–3, 600, 605 qualitative forecasting methods  545 quantile-quantile plots  231 quantitative forecasting methods  545 quartiles  96, 96–8, 100, 100–1 questionnaires 24–5 quota samples  17 R2 (coefficient of multiple determination)  511, 511–12, 537 random component  546, 546–7 random error  402, 418, 427, 439 random experiments  149 random numbers tables  18, 18–20 randomisation  350 randomised block design  415–23 between-block variation  416, 416, 417, 417–18, 439 between-group variation  402, 403, 416, 416, 417–18, 439 block effects  419–20, 421, 439 compared with completely randomised design 416 critical range  422–3, 439 defined  416 estimated relative efficiency  422, 439 F test statistic  419–20, 421, 439 focus of analysis  416 mean squares  418–19, 439 partitioning the total variation  416 random error  416, 416, 418, 439 tests for the treatment and block effects  416, 416–22, 421 total variation  416, 416–17, 439 Tukey procedure  422, 422–3 using statistical software  421, 446, 446 within-group variation  402 randomness  410, 420 range calculation of  99–100, 136 characteristics of  105 defined  46, 99 formula 131 interquartile  100, 100–1, 105 relevant range  463 rare events  60–1 rate of non-compliance  304–5 ratio scales  11, 11 RE (estimated relative efficiency)  422, 439 real-time monitoring  63 recoded variables  16 rectangular distribution  213, 233, 256 region of non-rejection  318, 318, 323, 324 region of rejection  318, 318, 318–19, 323, 324 regression analysis defined  456 ethical issues  493–4, 495, 496 pitfalls 493–4, 495, 496 predictions 462–3 scatter diagrams for  456–8, 457, 459 types of regression models  456–8, 458–9 see also multiple regression models; simple linear regression regression coefficients defined  459 interpreting 505–7, 507, 541–2, 588 net regression coefficients  506 partial regression coefficients  506 population regression coefficients  516–19, 517 producing a prediction line  461–2 testing for significance  484, 512, 513, 517, 517 using dummy variables  525–31, 526, 527, 529–30, 532, 587 regression models  456–8, 458–9 regression sum of squares (SSR)  467, 468, 468, 497, 522, 523 related populations  371–7, 374–6 relative frequency distributions  48, 48–9, 82, 215, 215 relevant range  463 repeated measurements  371 replicates  426 research findings, reporting of  351 Reserve Bank of Australia  14 residual  474, 497 residual analysis defined  473 multiple regression  514–15, 515–16, 543 simple linear regression  473–6, 474–6, 493–4, 495, 496 time-series forecasting models  579, 580, 606 using statistical software  475, 478–9, 503 residual error, measuring magnitude of  579–80 residual plots to assess linearity  474, 475 to detect autocorrelation  477–8, 479 for five forecasting methods  581, 582 multiple regression  514–15, 515–16 simple linear regression  494, 495, 496 resistant measures  101 respondent error  25 response 6 response variables  457 risk of Type II error (b)  320 road fatalities, statistics on  70–1, 70–1, 113–15 robust tests  337, 364 rules, of counting  168–71 sample coefficient of correlation  126, 126–8, 127, 131 sample covariance  123, 123–5, 131 sample mean  93, 93–4, 118, 130 sample proportion  340 sample size  254–5, 256, 323–4, 351 sample size determination in business  295 for the mean  294–6, 296, 308, 314 for the proportion  297–9, 298, 308, 314 using statistical software  296, 298, 314 sample space  149, 150 sample standard deviation  102, 102–3, 131, 334, 337 sample statistic  316, 332 sample variance  102, 103–4, 131 samples cluster  17, 21 convenience  17, 17 defined  8, 17 examples of  judgment  17, 17 non-probability  17, 17, 17–18 probability  17, 18 reasons for drawing  17 simple random  17, 18, 18–20 stratified  17, 21 systematic  17, 20, 20–1 Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e www.freebookslides.com INDEX sampling applications in auditing  300–7 Central Limit Theorem  214, 256, 256–8, 257 from finite populations  301, 307 from non-normally distributed populations 256–8, 257 from normally distributed populations  252–6, 253 with replacement  18 survey sampling methods  17–21 without replacement  18 sampling distributions defined  249 of the mean  249, 249–58, 253, 263 of the proportion  259–60, 260, 263 using statistical software  82, 265–6 sampling error  23, 25, 295 S&P 500 Index  596 S&P ASX 200 Index  596–7 SAS (software)  26 scales 11–12, 11–12 scatter diagrams defined  59, 456 example 59, 59 necessity of using  493–4 regression analysis  474–5, 493–4, 495, 496 regression models  456–8, 457, 459 sample coefficients of correlation  127 for two numerical variables  59, 59 using statistical software  87, 87–8 seasonal component  546, 546–7 seasonal data, time-series forecasting of  584–9, 585, 588, 600, 601, 606 second differences  561–3, 605 second-order autocorrelation  570 second-order autoregressive model  570–1, 571, 575, 575, 576, 577, 581, 600 second quartile  97 secondary sources, of data  13, 13–14 semi-structured data  15 separate-variance t test  365, 365–7, 367, 391, 397 shape  92, 107, 107–9, 136–7 shark attacks, statistics on  60–1 side-by-side bar charts  56, 56–7, 56–7, 87 significance level  319, 323–4, 350, 431 significance, statistical versus practical  351 simple events  149 simple linear regression  456–98 assumptions of  473, 473–6 calculating the slope  463–5, 497 calculating Y intercept  463–5, 497 coefficient of correlation  486, 497 coefficient of determination  469, 469–72, 470, 497 confidence interval estimate of the slope  485 confidence interval estimation for the mean of Y 489–91 defined  456 determining the equation  458–65, 459–62 Durbin–Watson statistic  475, 479, 479–80, 480, 497, 503 estimation of mean values  489–92 inferences about the slope  482–5, 483–5, 503 key formulas  497 least-squares method  459–61, 460, 460–1 measures of variation  467–72, 468–70, 497 measuring autocorrelation  477–8, 478–9, 503 pitfalls 493–4, 495, 496 prediction interval for an individual response Y  491, 491–2, 493 prediction line  459 regression coefficients  459, 461–2, 484 regression models  456–7, 456–8, 497 relevant range  463 residual analysis  473, 473–6, 474–6 standard error of the estimate  471, 471–2, 497 total sum of squares (SST)  467, 467–9, 468–9, 497 using statistical software  460–1, 461–2, 469, 472, 475, 483, 492, 492, 502, 502–3, 521 simple price index  591, 591–3, 601 simple random samples  17, 18, 18–20 single data value  skewed distribution  107, 107, 107–8, 109, 110, 137 slope calculating 497 confidence interval estimate of  485, 518–19, 537 F test for  484, 484–5, 484–5, 497 simple linear regression  463–5, 482–5, 483–5, 503 t test for  482, 482–3, 483, 497 testing for in multiple regression models 516–18, 517, 537 software, statistical  see statistical software spam filters  168–9 sparklines  64, 64, 88 spread (dispersion)  99 SPSS/PASW Statistics (software)  26 SS (sum of squares)  101 SSA (sum of squares due to factor A)  426, 426–7 SSAB (sum of squares due to interaction)  427 SSB (sum of squares between groups)  403, 407, 416, 416 SSB (sum of squares due to factor B)  427 SSBL (sum of squares between blocks)  416, 416, 417, 417–18 SSE (error sum of squares, or sum of squares error)  418, 467, 468, 468–9, 497, 581 SSE Composite Index  597 SSR (regression sum of squares)  467, 468, 468, 497, 522, 523 SST (sum of squares total, or total sum of squares)  403, 407, 416, 416, 467, 467–9, 468–9, 497 SSW (sum of squares within groups)  404, 407, 416, 416 stacked data  79 standard deviation of binomial distribution  194, 205 calculation of  101–2 characteristics of  105 chi-square test for  632–3, 632–3, 635 defined  101 in determining sample size  295 of the difference  302 of a discrete random variable  183, 183–4, 204 of exponential distribution  242 from a frequency distribution  118–19, 131 I-7 of hypergeometric distribution  201–2, 202, 205 of normal distribution  216, 216, 217, 222 sample standard deviation  102, 102–3 of the sum of two random variables  186, 186–7, 204 of uniform distribution  234 using statistical software  136–7 see also population standard deviation standard error defined 109 of the estimate  471, 471–2, 497, 580 of the mean  251, 251–2, 252, 263, 307 of the proportion  260, 307 standardised normal distribution  285, 285 standardised normal probability density function  217–18, 242 standardised normal random variables  216 Stata (software)  26 statistic, defined  8, statistical independence  159, 159–60, 173 statistical inference  280–1 statistical packages  26 statistical significance  351 statistical software analysis of variance  406, 408, 412, 430, 433–5, 444–7, 445–7 autoregressive modelling  575–7 bar charts and pie charts  79 binomial distribution  193, 193–4 bullet graphs  89–90 chi-square analysis  612–13, 618, 620, 625, 633, 641 confidence interval estimates  288, 289, 292, 313–14 contingency tables  86–7 cumulative distributions  82 descriptive statistics  109, 109, 135–8 determining sample size  296, 298 frequency distributions  80–2, 81 gauges 88–9 histograms 82–4 hypergeometric distribution  202, 202 hypothesis testing  326, 326, 331, 336–7, 336–8, 342, 356–7, 362–3, 367, 374, 376, 381, 386, 396–400, 397–400 Marascuilo procedure  620 measures of central tendency  135–6 multiple regression  507–8, 527, 527, 529–30, 532, 541–3, 542 normal distribution  226, 227, 246–7, 246–7 one-sample tests of hypothesis  356–7 organising numerical data  79–86 percentage and cumulative percentage polygons 85–6 percentage distributions  82 Poisson distribution  198 probabilities 178–9 probability distribution for a discrete variable 208 randomised block design  421 relative frequency  82 residual analysis  478–9 sample size determination  314 sampling distributions  265–6 scatter diagrams  87, 87–8 Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e www.freebookslides.com I-8 INDEX statistical software (continued) simple linear regression  460–1, 461–2, 469, 472, 475, 483, 492, 492, 502, 502–3, 521 sparklines 88 stacked and unstacked data  79 summary tables  77–8, 77–8 time-series forecasting  550, 552, 557–8, 569, 575–7, 582–3, 585, 588, 604, 604–6, 606 time-series plots  88 two-sample tests  396–400, 397–400 variation and shape  136–7 see also Microsoft Excel; Minitab; SAS; SPSS/ PASW; Stata statistics  6, 6–8, 26 Statistics New Zealand  stem-and-leaf displays  43, 43–5, 80, 350 straight-line relationship  456, 456 strata  21 stratified samples  17, 21 structured data  15 Studentised range distribution  409, 436 Student’s t distribution  285, 285, 285–6 subjective probability  149 subjectivity, in interpretation  129 sum of squares (SS)  101 sum of squares between blocks (SSBL) 416, 416, 417, 417–18 sum of squares between groups (SSB)  403, 407, 416, 416 sum of squares due to factor A (SSA)  426, 426–7 sum of squares due to factor B (SSB)  427 sum of squares due to interaction (SSAB)  427 sum of squares error (SSE)  418 see also error sum of squares sum of squares total (SST)  403, 407, 416, 416, 467, 467–9, 468–9 see also total sum of squares sum of squares within groups (SSW)  404, 407, 416, 416 summary tables ANOVA summary tables  405, 406–8, 408, 419, 430 defined  38 examples of  38–9 using statistical software  77–8, 77–8 see also frequency distributions survey errors  23–5 survey sampling methods  17–21 surveys  14, 22–5 symmetrical distribution  107, 107, 107–8, 109, 120 syndicated services  14 systematic samples  17, 20, 20–1 t distribution, properties of  285, 285–6 t test checking assumptions  337, 337–8 choice of  352 as a classical parametric procedure  337 for the correlation coefficient  486 critical value approach  334–6, 335 highest-order autoregressive model  571–2, 572, 601 of hypothesis for the mean (s unknown)  334, 334–7, 335–8, 353, 356 means of two independent populations (s unknown) 360–4, 361–4 p-value approach  336–7 paired t test  372, 372–6, 374–6, 398–9, 398–9 pooled-variance t test  360, 360–4, 361–4, 391, 396–7, 396–7 robustness of  337 separate-variance t test  365, 365–7, 367, 391, 397 for the slope  482, 482–3, 483, 497 t statistic and the F statistic  523, 537 test means of two related samples  372–6 tables for categorical data  38–42 choosing an appropriate chart  73 frequency distributions  46–8 for numerical data  43–50 of random numbers  18, 18–20 using statistical software for  77–8, 77–8 see also contingency tables; summary tables telephone polling  12 test statistic  318, 323–4, 334 tests goodness-of-fit tests  627, 627–31, 635 power of  344–7, 344–8 robust tests  337, 364 see also hypothesis testing; one-sample tests; one-tail tests; t test; two-sample tests; twotail tests; Z test third-order autoregressive model  576 third (upper) quartile  97, 100, 130 tied observations  10 time-period forecasting  553, 600 time series  545 time-series forecasting  545–601 assumptions of  546, 599 autoregressive modelling  570, 570–8, 573, 575–8, 581, 582–3, 600–1, 605–6 in business  545 choosing an appropriate model  579–81, 580, 582–3, 606 classical multiplicative model  546, 546–7, 585, 600 defined  545 exponential smoothing  551, 551–3, 552, 600, 604 exponential trend model  558, 558–60, 560–1, 581, 582–3, 585–8, 588, 600–1, 605 five methods compared  581, 582–3, 606 forecasting time period  600 Holt–Winters method  567, 567–8, 569, 581, 582–3, 600 index numbers  591, 591–7 key formulas  600–1 least-squares method  555–63, 581, 582–3 least-squares trend-fitting and forecasting 555–63, 557, 585–9, 588, 605 linear trend model  555, 555–6, 557, 561–2, 581, 582–3, 600, 605 mean absolute deviation (MAD)  580 model selection  561–3, 571–2, 579–81, 580, 582–3, 605 moving averages  548, 548–51, 550 performing a residual analysis  579, 580 pitfalls 599 principle of parsimony  581 quadratic trend model  557, 557–8, 558–9, 562, 581, 582–3, 600, 605 as a quantitative method  545 of seasonal data  584–9, 585, 588, 600, 606 smoothing the annual time series  547–53 using statistical software  550, 552, 557–8, 569, 575–7, 582–3, 585, 588, 604, 604–6, 606 time-series plots  59, 59–61, 60–1, 88, 548 total amount  300, 300–2, 314 total difference  303–4, 314 total sum of squares (SST)  403, 407, 416, 416, 467, 467–9, 468–9, 497 total variation  403, 403, 403–4, 416, 416–17, 426, 426, 439, 467 trade associations  14 transformation formula  216, 216–19, 217–19, 224 treatment effect  402, 404–6, 416, 416–22, 421 treemaps  65, 65, 65–6 trend 545–6, 546 trend component  546 trend-fitting  see least-squares trend-fitting and forecasting triple exponential smoothing  555 Tukey–Kramer multiple comparison procedure  408, 408–10, 410, 413, 435, 439, 445 Tukey procedure  422, 422–3, 435–6 two-factor factorial design  425 two-sample tests  359–400 comparing the means of two independent populations 359–68, 361–4, 367 comparing the means of two related populations 371–7, 374–6 comparing two population proportions  384–7, 385–6 F test for difference between two variances 378–83, 379, 381–2 flow chart for selecting  380 using statistical software  396–400, 397–400 two-tail tests autoregressive modelling  573, 577 choice of  350 defined  322 difference between two means  361–2, 362 difference between two proportions  364–5 ethical considerations  350 F test for difference between two variances  379, 382 hypothesis for the proportion  342 p-value approach  325–6, 326, 342, 342–3 paired t test  372–3 t test of hypothesis for the mean  334–6, 335 two-way analysis of variance  425–36 critical range  438, 440 defined  425 F test for factor A effect  428, 440 F test for factor B effect  428, 428–9, 440 F test for interaction effect  429, 429–30, 440 factor A variation  426–8, 436, 439 factor B variation  426–8, 436, 439 interaction variation  439 interpreting interaction effects  432–5, 432–5 key formulas  439–40 mean squares  428, 439 random error  427, 439 summary tables  430 testing for factor and interaction effects  426, 426–32, 430–1 Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e www.freebookslides.com INDEX total variation  426, 426, 439 Tukey procedure  435–6 using statistical software  430, 433–5, 446–7, 446–7 Type I errors  319, 319–21, 344 Type II errors  319, 319–21, 344, 345–6, 345–6 unbiased sample mean  249, 249–51, 250 UNDP (United Nations Development Programme) 458 unethical practices  see ethical issues unexplained variation  467 uniform distribution  213, 214, 233, 233–4, 234, 242, 256, 257, 258 uniform probability density function  233–4, 234, 242 United Nations Development Programme (UNDP) 458 United States Federal Census  26 unstacked data  79 unstructured data  15 unweighted aggregate price index  593, 593–4, 601 upper quartile  97, 100 values 6, 16 variables categorical 9–10, 10, 10, 55–7, 86–7, 527–8 continuous  10 defined  dependent  456, 507–8, 508 discrete  10, 181–4 dummy variables  525–31, 526, 527, 529–30, 532, 587 explanatory  457 independent  456, 506–7, 520, 523–4, 528–9, 535–6, 537 lagged predictor variables  605 numerical 9–10, 10, 10 operational definition  recoding 16 response variable  457 types of association  125, 125 variance analysis of variance (ANOVA)  402 calculation of  103–5 characteristics of  105 chi-square test for  632–3, 632–3, 635 defined  101 difference between two means, unequal variances 397–8 of discrete random variables  183, 183–4, 204 equal variance  476, 476 exponential distribution  236, 242 F test for difference between two variances 378–83, 379, 381–2, 399–400, 399–400 from a frequency distribution  118 homogeneity of  411, 412, 445 population variance  114, 114–15 sample variance  102, 103–4 of the sum of two random variables  186, 186–7, 204 uniform distribution  233, 242 using statistical software  136–7, 399–400, 399–400 see also one-way analysis of variance; two-way analysis of variance variance inflationary factor (VIF)  535, 535–6, 537 variation calculating with Excel  136–7 coefficient of  105, 105–6 defined  92 explained variation  467 measures of  99–105, 467–72, 468–70, 497, 502–3 I-9 partitioning the total variation  403, 426 total variation  403, 403, 403–4, 416, 416–17, 426, 426, 439, 467 unexplained  467 Venn diagrams  150, 150–1, 151 VIF (variance inflationary factor)  535, 535–6, 537 wage price index  505 WaldoLands 63, 64, 65, 65 weighted aggregate price indices  594, 594–6 Wilcoxon rank sum test  364 within-group variation  402, 404, 439 _ X bar (X )  93, 252–3, 255–6, 257, 263 X values  223–6, 224–5, 242 Y intercept  457, 460–1, 461, 463–5, 497 Z scores  106, 106–7, 131, 136–7, 214, 216, 231 Z test for the difference between two means  359, 391 for the difference between two proportions  384, 384–7, 385–6, 391, 400, 400, 612–13 for the difference between two related populations 371–7, 374–6 of hypothesis for the mean  322, 322–8, 323, 326, 337, 353, 356 for the mean difference  371–2, 391 for the population mean  344, 344 for the proportion  340, 340–3, 341, 342, 352, 353, 357 versus t test  337 Z test statistic  322, 323–4, 325 Z values  224–5, 224–6, 231, 242, 263 Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd) 2019— 9781488617249 — Berenson/Basic Business Statistics 5e www.freebookslides.com This page is intentionally left blank ... published by Prentice Hall, including Statistics for Managers Using Microsoft Excel, Basic Business Statistics: Concepts and Applications and Business Statistics: A First Course Over the years, Berenson. .. Pty Ltd) 2019— 9781488617249 — Berenson /Basic Business Statistics 5e ix preface This fifth Australasian and Pacific edition of Basic Business Statistics: Concepts and Applications continues to... statistics education and is the co-author of 14 books, including such best-selling statistics textbooks as Statistics for Managers Using Microsoft Excel, Basic Business Statistics: Concepts and