 10.5.1E: The thickness specification for aluminum sheets is 0.2460.254 mm. ...
 10.5.2E: The specification for the diameters of ball bearings is 15.4015.60...
 10.5.3E: Refer to Exercise 2.a. To what value should the process mean be set...
 10.5.4E: Refer to Exercise 1.a. To what value should the process mean be set...
 10.5.5E: A Process has process capacity index of CP =1.2.a. Assume the proce...
Solutions for Chapter 10.5: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists  4th Edition
ISBN: 9780073401331
Solutions for Chapter 10.5
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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

Alternative hypothesis
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.

Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability

Backward elimination
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

Biased estimator
Unbiased estimator.

Bivariate normal distribution
The joint distribution of two normal random variables

Categorical data
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

Causal variable
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

Conditional probability
The probability of an event given that the random experiment produces an outcome in another event.

Conditional variance.
The variance of the conditional probability distribution of a random variable.

Control chart
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the incontrol 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 incontrol, or free from assignable causes. Points beyond the control limits indicate an outofcontrol process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

Correction factor
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 .

Critical value(s)
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.

Defect
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

Error variance
The variance of an error term or component in a model.

False alarm
A signal from a control chart when no assignable causes are present

Gaussian distribution
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

Geometric mean.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .

Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.