- 10.1.1: In an experiment to compare the tensile strengths ofI 5 5 different...
- 10.1.2: Suppose that the compression-strength observations onthe fourth typ...
- 10.1.3: The lumen output was determined for each of I 5 3 differentbrands o...
- 10.1.4: It is common practice in many countries to destroy(shred) refrigera...
- 10.1.5: Consider the following summary data on the modulus ofelasticity (3 ...
- 10.1.6: The article Origin of Precambrian Iron Formations(Econ. Geology, 19...
- 10.1.7: An experiment was carried out to compare electricalresistivity for ...
- 10.1.8: A study of the properties of metal plate-connectedtrusses used for ...
- 10.1.9: Six samples of each of four types of cereal grain grownin a certain...
- 10.1.10: In single-factor ANOVA with I treatments and J observationsper trea...
Solutions for Chapter 10.1: Single-Factor ANOVA
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with 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).
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 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
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
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.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
A probability distribution for a continuous random variable.
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.
See Control chart.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
A matrix that provides the tests that are to be conducted in an experiment.
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
A study in which a sample from a population is used to make inference to the population. See Analytic study
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 property of a collection of events that indicates that their union equals the sample space.
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
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