- 8.2.1: In an experiment to determine factors related to weld toughness, th...
- 8.2.2: In a laboratory test of a new engine design, the emissions rate (in...
- 8.2.3: Two chemical engineers, A and B, are working independently to devel...
- 8.2.4: The article Influence of Freezing Temperature on Hydraulic Conducti...
- 8.2.5: Refer to Exercise 10 in Section 7.4. a. Divide the data into two gr...
- 8.2.6: The following table lists values for three variables measured for 6...
Solutions for Chapter 8.2: Confounding and Collinearity
Full solutions for Statistics for Engineers and Scientists | 4th 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.
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.
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.
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
The mean of the conditional probability distribution of a random variable.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete 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
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
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.
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
Discrete random variable
A random variable with a inite (or countably ininite) range.
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.
A signal from a control chart when no assignable causes are present
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
Fraction defective control chart
See P chart