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# Solutions for Chapter 2.2: Counting Methods

## Full solutions for Statistics for Engineers and Scientists | 4th Edition

ISBN: 9780073401331

Solutions for Chapter 2.2: Counting Methods

Solutions for Chapter 2.2
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##### ISBN: 9780073401331

Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Chapter 2.2: Counting Methods includes 12 full step-by-step solutions. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Since 12 problems in chapter 2.2: Counting Methods have been answered, more than 262761 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
• Attribute

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.

• 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.

• Bernoulli trials

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

• Block

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.

• Categorical data

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

• 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.

• Completely randomized design (or experiment)

A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

• 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.

• Continuity correction.

A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

• Cook’s distance

In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

• Defects-per-unit control chart

See U chart

• Deming

W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

• Error mean square

The error sum of squares divided by its number of degrees of freedom.

• Error sum of squares

In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.

• Estimate (or point estimate)

The numerical value of a point estimator.

• Event

A subset of a sample space.

• Exhaustive

A property of a collection of events that indicates that their union equals the sample space.

• Fraction defective

In statistical quality control, that portion of a number of units or the output of a process that is defective.

• Gamma random variable

A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

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