- 6.1.1E: In an experiment to measure the lifetimes of parts manufactured fro...
- 6.1.2E: A simple random sample consists of 65 lengths of piano wire that we...
- 6.1.3E: The article “Supply Voltage Quality in Low-Voltage Industrial Netwo...
- 6.1.4E: The pH of an acid solution used to etch aluminum varies somewhat fr...
- 6.1.5E: Recently many companies have been experimenting with telecommuting,...
- 6.1.6E: A certain type of stainless steel powder is supposed to have a mean...
- 6.1.7E: When it is operating properly, a chemical plant has a mean daily pr...
- 6.1.8E: Lasers can provide highly accurate measurements of small movements....
- 6.1.9E: The article "Predicting Profit Performance for Selecting Candidate ...
- 6.1.10E: A new concrete mix is being designed to provide adequate compressiv...
- 6.1.11E: Fill in the blank: If the null hypothesis is H0: µ. ? 5, then the m...
- 6.1.12E: Fill in the blank: In a test of H0: ? 10 versus H\-.fi<10, the samp...
- 6.1.13E: An engineer takes a large number of independent measurements of the...
- 6.1.14E: The following MINITAB output presents the results of a hypothesis t...
- 6.1.15E: The following MINITAB output presents the results of a hypothesis t...
Solutions for Chapter 6.1: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists | 4th Edition
2 k factorial experiment.
A full factorial experiment with k factors and 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 qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.
See Arithmetic mean.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
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.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.
Coeficient of determination
See R 2 .
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.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
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 term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
Cumulative sum control chart (CUSUM)
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 subset of effects in a fractional factorial design that deine the aliases in the design.
The response variable in regression or a designed experiment.
A study in which a sample from a population is used to make inference to the population. See Analytic study
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.