- Chapter 1: Statistics: The Art and Science of Data
- Chapter 10: Inference in Practice
- Chapter 2: Describing Distributions of Data
- Chapter 3: Modeling Distributions of Data
- Chapter 4: Describing Relationships
- Chapter 5: Sampling and Surveys
- Chapter 6: Designing Experiments
- Chapter 7: Probability: What Are the Chances?
- Chapter 8: Probability Models
- Chapter 9: ntroduction to Inference
Statistics Through Applications 2nd Edition - Solutions by Chapter
Full solutions for Statistics Through Applications | 2nd Edition
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.
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test
Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
The joint probability distribution of two random variables.
Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
The probability of an event given that the random experiment produces an outcome in another event.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
The variance of the conditional probability distribution of a random variable.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
Formulas used to determine the number of elements in sample spaces and events.
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
Discrete random variable
A random variable with a inite (or countably ininite) range.
Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
A subset of a sample space.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.