- Chapter 1: Introduction to Statistics
- Chapter 1.2: Statistical and Critical Thinking
- Chapter 1.3: Types of Data
- Chapter 1.4: Collecting Sample Data
- Chapter 10: Correlation and Regression
- Chapter 10.2: Correlation
- Chapter 10.3: Regression
- Chapter 10.4: Rank Correlation
- Chapter 11: Chi-Square and Analysis of Variance
- Chapter 11.2: Goodness-of-Fit
- Chapter 11.3: Contingency Tables
- Chapter 11.4: Analysis of Variance
- Chapter 2: Summarizing and Graphing Data
- Chapter 2.2: Frequency Distributions
- Chapter 2.3: Histograms
- Chapter 2.4: Graphs That Enlighten and Graphs That Deceive
- Chapter 3: Statistics for Describing, Exploring, and Comparing Data
- Chapter 3.2: Measures of Center
- Chapter 3.3: Measures of Variation
- Chapter 3.4: Measures of Relative Standing and Boxplots
- Chapter 4: Probability
- Chapter 4.2: Basic Concepts of Probability
- Chapter 4.3: Addition Rule
- Chapter 4.4: Multiplication Rule: Basics
- Chapter 4.5: Multiplication Rule: Complements and Conditional Probability
- Chapter 4.6: Counting
- Chapter 5: Discrete Probability Distributions
- Chapter 5.2: Probability Distributions
- Chapter 5.3: Binomial Probability Distributions
- Chapter 5.4: Parameters for Binomial Distributions
- Chapter 6: Normal Probability Distributions
- Chapter 6.2: The Standard Normal Distribution
- Chapter 6.3: Applications of Normal Distributions
- Chapter 6.4: Sampling Distributions and Estimators
- Chapter 6.5: The Central Limit Theorem
- Chapter 6.6: Assessing Normality
- Chapter 6.7: Normal as Approximation to Binomial
- Chapter 7: Estimates and Sample Sizes
- Chapter 7.2: Estimating a Population Proportion
- Chapter 7.3: Estimating a Population Mean
- Chapter 7.4: Estimating a Population Standard Deviation or Variance
- Chapter 8: Hypothesis Testing
- Chapter 8.2: Basics of Hypothesis Testing
- Chapter 8.3: Testing a Claim About a Proportion
- Chapter 8.4: Testing a Claim about a Mean
- Chapter 8.5: Testing a Claim About a Standard Deviation or Variance
- Chapter 9: Inferences from Two Samples
- Chapter 9.2: Two Proportions
- Chapter 9.3: Two Means: Independent Samples
- Chapter 9.4: Two Dependent Samples (Matched Pairs)
Essentials of Statistics 5th Edition - Solutions by Chapter
Full solutions for Essentials of Statistics | 5th Edition
a-error (or a-risk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).
Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
The joint probability distribution of two random variables.
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
Error of estimation
The difference between an estimated value and the true value.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
Fraction defective control chart
See P chart
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function