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Solutions for Chapter 12: The Practice of Statistics 4th Edition
Full solutions for The Practice of Statistics | 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).
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.
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
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.
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
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.
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 variance of the conditional probability distribution of a random variable.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
Error of estimation
The difference between an estimated value and the true value.
A series of tests in which changes are made to the system under study
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