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

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.

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

The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

A distribution with two modes

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

Another term for the conidence coeficient.

A random variable with an interval (either inite or ininite) of real numbers for its range.

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.

A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

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

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

A discrete random variable with a inite range and constant probability mass function.

Another name for a cumulative distribution function.

A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

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.

In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

A discrete random variable that is the number of Bernoulli trials until a success occurs.