Basic Statistics for Business and Economics 9e by Lind, Marchal, Wathen

Basic Statistics for Business and Economics 9e by Lind, Marchal, Wathen is the 9th edition of the Basic Statistics for Business & Economics textbook authored by Douglas A. Lind, Coastal Carolina University and The University of Toledo, William G. Marchal, The University of Toledo, and Samuel A. Wathen, Coastal Carolina University, and published by McGraw-Hill Education, New York, NY in 2019.

• Alternate hypothesis. A statement that is accepted if the sample data provide sufficient evidence that the null hypothesis is false.
• Analysis of variance (ANOVA). A technique used to test simultaneously whether the means of several populations are equal. It uses the F distribution as the distribution of the test statistic.
• Autocorrelation. Successive residuals in a time series are correlated.
• Bar chart. A graph that shows qualitative classes on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are proportional to the heights of the bars.
• Binomial probability distribution. A probability distribution based on a discrete random variable. Its major characteristics are: 1. An outcome on each trial of an experiment is classified into one of two mutually exclusive categories—a success or a failure. 2. The random variable is the number of successes in a fixed number of trials. 3. The probability of success is the same for each trial. 4. The trials are independent, meaning that the outcome of one trial does not affect the outcome of any other trial.
• Box plot. A graphic display that shows the general shape of a variable's distribution. It is based on five descriptive statistics: the maximum and minimum values, the first and third quartiles, and the median.
• Cause-and-effect diagram. A diagram used to illustrate the relationship between a problem and a set of the problem's possible causes.
• Central limit theorem. If all samples of a particular size are selected from any population, the sampling distribution of the sample mean is approximately a normal distribution. This approximation improves with larger samples.
• Chebyshev's theorem. For any set of observations (sample or population), the proportion of the values that lie within k standard deviations of the mean is at least 1 − 1/k2, where k is any value greater than 1.
• Classical probability. Probability based on the assumption we know the number of possible outcomes and that each of the outcomes is equally likely.
• Cluster sampling. A population is divided into clusters using naturally occurring geographic or other boundaries. Then, clusters are randomly selected and a sample is collected by randomly selecting from each cluster.
• Coefficient of determination. The proportion of the total variation in the dependent variable Y that is explained, or accounted for, by the variation in the independent variable X.
• Coefficient of multiple determination. The percent of variation in the dependent variable, y, explained by the set of independent variables, x1, x2, x3, . . . xk.
• Collectively exhaustive. At least one of the events must occur when an experiment is conducted.
• Combination formula. A formula to count the number of possible arrangements when the order of the outcomes is not important. For example, the outcome {a, b, c} is considered the same as {c, b, a}.
• Conditional probability. The probability of a particular event occurring, given that another event has occurred.
• Confidence interval. A range of values constructed from sample data so that the population parameter is likely to occur within that range at a specified probability. The specified probability is called the level of confidence.
• Contingency table. A table used to classify sample observations according to two identifiable characteristics.
• Continuous random variable. A random variable that may assume an infinite number of values within a given range.
• Correlation analysis. A group of techniques to measure the relationship between two variables.
• Correlation coefficient. A measure of the strength of the linear relationship between two variables.
• Critical value. The dividing point between the region where the null hypothesis is rejected and the region where it is not rejected.
• Deciles. Values of an ordered (minimum to maximum) data set that divide the data into 10 equal parts.
• Dependent variable. The variable that is being predicted or estimated.
• Descriptive statistics. Methods of organizing, summarizing, and presenting data in an informative way.
• Discrete random variable. A random variable that can assume only certain clearly separated values.
• Dot plot. A dot plot summarizes the distribution of one variable by stacking dots at points on a number line that shows the values of the variable. A dot plot shows all values.
• Dummy variable. A variable in which there are only two possible outcomes. For analysis, one of the outcomes is coded a 1 and the other a 0.
• Empirical probability. The probability of an event happening is the fraction of the time similar events happened in the past.
• Empirical Rule. For a symmetrical, bell-shaped frequency distribution, approximately 68% of the observations lie within plus and minus one standard deviation of the mean; about 95% of the observations lie within plus and minus two standard deviations of the mean; and practically all (99.7%) lie within plus and minus three standard deviations of the mean.
• Event. A collection of one or more outcomes of an experiment.
• Experiment. A process that leads to the occurrence of one and only one of several possible results.
• Frequency distribution. A grouping of quantitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class.
• Frequency table. A grouping of qualitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class.
• Global test. A test used to determine if any of the set of independent variables has regression coefficients different from zero.
• Histogram. A graph in which the classes are marked on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are represented by the heights of the bars, and the bars are drawn adjacent to each other.
• Homoscedasticity. The variation around the regression equation is the same for all of the values of the independent variables.
• Hypothesis. A statement about a population parameter subject to verification.
• Hypothesis testing. A procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement.
• Independence. The occurrence of one event has no effect on the probability of the occurrence of another event.
• Independent variable. A variable that provides the basis for estimation.
• Inferential statistics. The methods used to estimate a property of a population on the basis of a sample.
• Interquartile range. The absolute numerical difference between the first and third quartiles. Fifty percent of a distribution's values occur in this range.
• Interval level of measurement. For data recorded at the interval level of measurement, the interval or the distance between values is meaningful. The interval level of measurement is based on a scale with a known unit of measurement.
• Joint probability. A probability that measures the likelihood two or more events will happen concurrently.
• Law of large numbers. Over a large number of trials, the empirical probability of an event will approach its true probability.
• Least squares principle. A mathematical procedure that uses the data to position a line with the objective of minimizing the sum of the squares of the vertical distances between the actual y values and the predicted values of y.
• Level of significance. The probability of rejecting the null hypothesis when it is true.
• Measure of dispersion. A value that shows the spread of a data set. The range, variance, and standard deviation are measures of dispersion.
• Measure of location. A single value that is typical of the data. It pinpoints the center of a distribution. The arithmetic mean, weighted mean, median, mode, and geometric mean are measures of location.
• Median. The midpoint of the values after they have been ordered from the minimum to the maximum values.
• Mode. The value of the observation that appears most frequently.
• Multiplication formula. If there are m ways of doing one thing and n ways of doing another thing, there are m × n ways of doing both.
• Mutually exclusive. The occurrence of one event means that none of the other events can occur at the same time.
• Nominal level of measurement. Data recorded at the nominal level of measurement are represented as labels or names. They have no order. They can only be classified and counted.
• Null hypothesis. A statement about the value of a population parameter developed for the purpose of testing numerical evidence.
• Ordinal level of measurement. Data recorded at the ordinal level of measurement are based on a relative ranking or rating of items based on a defined attribute or qualitative variable. Variables based on this level of measurement are only ranked or counted.
• Outcome. A particular result of an experiment.
• Outlier. A data point that is unusually far from the others. An accepted rule is to classify an observation as an outlier if it is 1.5 times the interquartile range above the third quartile or below the first quartile.
• p-value. The probability of observing a sample value as extreme as, or more extreme than, the value observed, given that the null hypothesis is true.
• Parameter. A characteristic of a population.
• Percentiles. Values of an ordered (minimum to maximum) data set that divide the data into 100 intervals.
• Permutation. Any arrangement of r objects selected from a single group of n possible objects.
• Permutation formula. A formula to count the number of possible arrangements when the order of the outcomes is important. For example, the outcome {a, b, c} is considered different from {c, b, a}.
• Pie chart. A chart that shows the proportion or percentage that each class represents of the total number of frequencies.
• Point estimate. The statistic, computed from sample information, that estimates a population parameter.
• Poisson experiment. An experiment where the random variable is the number of times an outcome is observed in a clearly defined interval. Examples of an interval include time, distance, area, or volume. In addition, the experiment requires that the probability of an outcome is proportional to the length of the interval, and the outcomes in each interval are independent.
• Poisson probability distribution. A mathematical function used to calculate the probabilities of a Poisson experiment, where the random variable is the number of times an outcome occurs in a clearly defined interval, the probability of an outcome is proportional to the length of the interval, and the intervals are independent.
• Population. The entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest.
• Probability. A value between 0 and 1, inclusive, describing the relative possibility (chance or likelihood) an event will occur.
• Probability distribution. A listing of all the outcomes of an experiment and the probability associated with each outcome.
• Proportion. The fraction, ratio, or percent indicating the part of the sample or the population having a particular trait of interest.
• Qualitative variables. A nominal-scale variable coded to assume only one nonnumeric outcome or category. For example, a person is considered either employed or unemployed.
• Quartiles. Values of an ordered (minimum to maximum) data set that divide the data into four intervals.
• Random variable. A variable measured or observed as the result of an experiment. By chance, the variable can have different values.
• Random variation. The sum of the squared differences between each observation and its treatment mean.
• Range. A measure of dispersion found by subtracting the minimum value from the maximum value.
• Ratio level of measurement. Data recorded at the ratio level of measurement are based on a scale with a known unit of measurement and a meaningful interpretation of zero on the scale.
• Regression equation. An equation that expresses the linear relationship between two variables.
• Residual. The difference between the actual value of the dependent variable and the estimated value of the dependent variable, that is, y − y^.
• Sample. A portion, or part, of the population of interest.
• Sampling distribution of the sample mean. A probability distribution of all possible sample means of a given sample size.
• Sampling error. The difference between a sample statistic and its corresponding population parameter.
• Scatter diagram. Graphical technique used to show the relationship between two variables measured with interval or ratio scales.
• Simple random sample. A sample selected so that each item or person in the population has the same chance of being included.
• Special rule of addition. A rule used to find the probabilities of events made up of A or B when the events are mutually exclusive.
• Special rule of multiplication. A rule used to find the probability of the joint occurrence of independent events.
• Standard error of estimate. A measure of the dispersion, or scatter, of the observed values around the line of regression for a given value of x.
• Statistic. A characteristic of a sample.
• Statistics. The science of collecting, organizing, presenting analyzing, and interpreting data to assist in making more effective decisions.
• Stepwise regression. A step-by-step method to determine a regression equation that begins with a single independent variable and adds or deletes independent variables one by one. Only independent variables with nonzero regression coefficients are included in the regression equation.
• Stratified random sample. A population is divided into subgroups, called strata, and a sample is randomly selected from each stratum.
• Subjective concept of probability. The likelihood (probability) of a particular event happening that is assigned by an individual based on whatever information is available.
• Systematic random sampling. A random starting point is selected, and then every kth member of the population is selected.
• Test statistic. A value, determined from sample information, used to decide whether to reject the null hypothesis.
• Total variation. The sum of the squared differences between each observation and the overall mean.
• Treatment variation. The sum of the squared differences between each treatment mean and the grand or overall mean. Each squared difference is multiplied by the number of observations in the treatment.
• Type I error. Rejecting the null hypothesis, H0, when it is true.
• Type II error. Not rejecting the null hypothesis when it is false.
• Variance. The arithmetic mean of the squared deviations from the mean.
• Variance inflation factor. A test used to detect correlation among independent variables.
• z value. The signed distance between a selected value, designated x, and the mean, μ, divided by the standard deviation, σ. Also called z score.