Introduction to Statistics and Data Analysis (with CengageNOW Printed Access Card) (Available Titles CengageNOW) 3rd Edition - Solutions by Chapter

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

A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

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.

The joint probability distribution of two random variables.

The joint distribution of two normal random variables

When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

The probability of an event given that the random experiment produces an outcome in another event.

In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

An expression sometimes used for nonlinear regression models or polynomial regression models.

An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

The amount of variability exhibited by data

The error sum of squares divided by its number of degrees of freedom.

A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

A subset of a sample space.

A property of a collection of events that indicates that their union equals the sample space.

A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .