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Solutions for Chapter SE4: Sample Exams

Full solutions for Probability and Statistics for Engineering and the Sciences (with Student Suite Online) | 7th Edition

ISBN: 9780495382171

Solutions for Chapter SE4: Sample Exams

Solutions for Chapter SE4
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ISBN: 9780495382171

This expansive textbook survival guide covers the following chapters and their solutions. Probability and Statistics for Engineering and the Sciences (with Student Suite Online) was written by and is associated to the ISBN: 9780495382171. Chapter SE4: Sample Exams includes 23 full step-by-step solutions. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences (with Student Suite Online), edition: 7. Since 23 problems in chapter SE4: Sample Exams have been answered, more than 21363 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
• 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

• Assignable cause

The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

• Average

See Arithmetic mean.

• Bayes’ theorem

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

• Biased estimator

Unbiased estimator.

• Center line

A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

• Coeficient of determination

See R 2 .

• Conditional probability mass function

The probability mass function of the conditional probability distribution of a discrete random variable.

• Confounding

When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

• Contingency table.

A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

• Continuity correction.

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

• Contour plot

A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

• Control chart

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.

• 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.

• Design matrix

A matrix that provides the tests that are to be conducted in an experiment.

• Discrete random variable

A random variable with a inite (or countably ininite) range.

• Error of estimation

The difference between an estimated value and the true value.

• Extra sum of squares method

A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

• F distribution.

The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.

• Fisher’s least signiicant difference (LSD) method

A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.

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