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# Solutions for Chapter 15.7: Applied Statistics and Probability for Engineers 6th Edition

## Full solutions for Applied Statistics and Probability for Engineers | 6th Edition

ISBN: 9781118539712

Solutions for Chapter 15.7

Solutions for Chapter 15.7
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##### ISBN: 9781118539712

This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 15.7 includes 14 full step-by-step solutions. Since 14 problems in chapter 15.7 have been answered, more than 173348 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
• `-error (or `-risk)

In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

• Alias

In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Arithmetic mean

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.

• Bayes’ theorem

An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).

• Cause-and-effect diagram

A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

• 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.

• Consistent estimator

An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

• Continuous distribution

A probability distribution for a continuous random variable.

• Control limits

See Control chart.

• Correlation matrix

A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .

• Counting techniques

Formulas used to determine the number of elements in sample spaces and events.

• Covariance matrix

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.

• Defects-per-unit control chart

See U chart

• Distribution free method(s)

Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

• Error mean square

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

• Experiment

A series of tests in which changes are made to the system under study

• Factorial experiment

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.

• Generating function

A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function

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