Solutions for Chapter 5: USING EQUATIONS TO SOLVE BUSINESS PROBLEMS

A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

The mean 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

An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

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 the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

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.

A subset of effects in a fractional factorial design that deine the aliases in the design.

W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

Another name for a probability density function

A signal from a control chart when no assignable causes are present

A term in the formula for the variance of a hypergeometric random variable.

A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.

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.

In statistical quality control, that portion of a number of units or the output of a process that is defective.

Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.

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