Solutions for Chapter 5: Summarizing Bivariate Data

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 portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

Any control chart for a discrete random variable. See Variables control chart.

An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

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

A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

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 correction factor used to improve the approximation to binomial probabilities from a normal distribution.

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.

The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

A quality tool that graphically shows the location of defects on a part or in a process.

A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

The variance of an error term or component in a model.

The numerical value of a point estimator.

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.

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

A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function

In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.