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# Solutions for Chapter 9.4: More Tests

## Full solutions for Probability and Statistical Inference | 9th Edition

ISBN: 9780321923271

Solutions for Chapter 9.4: More Tests

Solutions for Chapter 9.4
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##### ISBN: 9780321923271

This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. Chapter 9.4: More Tests includes 18 full step-by-step solutions. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. Since 18 problems in chapter 9.4: More Tests have been answered, more than 92228 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

• `-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).

• 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

• Biased estimator

Unbiased estimator.

• Categorical data

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

• Conditional probability mass function

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

• Conditional variance.

The variance of the conditional probability distribution of a 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.

• Continuous distribution

A probability distribution for a continuous random variable.

• 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 .

• Defect concentration diagram

A quality tool that graphically shows the location of defects on a part or in a process.

• Deining relation

A subset of effects in a fractional factorial design that deine the aliases in the design.

• Discrete random variable

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

• 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.

• Error variance

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

• Estimate (or point estimate)

The numerical value of a point estimator.

• Finite population correction factor

A term in the formula for the variance of a hypergeometric random variable.

• First-order model

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

• 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

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