- 7.3.1E: ?A chemical reaction is run 12 times, and the temperature xi (in °C...
- 7.3.3E: Ozone (O3) is a major component of air pollution in many cities. At...
- 7.3.4E: In a study similar to the one in Exercise 3, the relative humidity ...
- 7.3.5E: ?Refer to Exercises 3 and 4. An atmospheric scientist notices that ...
- 7.3.7E: The coefficient of absorption (COA) for a clay brick is the ratio o...
- 7.3.8E: ?The article “Application of Radial Basis Function Neural Networks ...
- 7.3.9E: ?In a study to determine the relationship between ambient outdoor t...
- 7.3.10E: Three engineers are independently estimating the spring constant of...
- 7.3.12E: Refer to Exercise 1. If 95% confidence intervals are constructed fo...
- 7.3.13E: ?In a study of copper bars, the relationship between shear stress i...
- 7.3.14E: ?In the manufacture of synthetic fiber, the fiber is often “set” by...
- 7.3.15E: In the following MINITAB output, some of the numbers have been acci...
- 7.3.16E: In the following MINITAB output, some of the numbers have been acci...
Solutions for Chapter 7.3: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists | 4th Edition
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.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
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.
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.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
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.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Another name for a cumulative distribution function.
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
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 series of tests in which changes are made to the system under study
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
Goodness of fit
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.