- 5.5.1: In a test of the effect of dampness on electric connections, 100 el...
- 5.5.2: The specification for the pull strength of a wire that connects an ...
- 5.5.3: The specification for the pull strength of a wire that connects an ...
- 5.5.4: A group of 50 computer science students were taught introductory co...
- 5.5.5: Crash testing is a highly expensive procedure to evaluate the abili...
- 5.5.6: The article Occurrence and Distribution of Ammonium in Iowa Groundw...
- 5.5.7: In a study of contamination at landfills containing construction an...
- 5.5.8: The article Case Study Based Instruction of DOE and SPC (J. Brady a...
- 5.5.9: A mobile computer network consists of a number of computers (called...
- 5.5.10: The article Evaluation of Criteria for Setting Speed Limits on Grav...
- 5.5.11: In a certain year, there were 80 days with measurable snowfall in D...
Solutions for Chapter 5.5: Confidence Intervals for the Difference Between Two Proportions
Full solutions for Statistics for Engineers and Scientists | 4th Edition
Solutions for Chapter 5.5: Confidence Intervals for the Difference Between Two ProportionsGet Full Solutions
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.
All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions
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.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
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 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.
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 .
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.
Another name for a probability density function
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
The amount of variability exhibited by data
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
A subset of a sample space.
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
In statistical quality control, that portion of a number of units or the output of a process that is defective.