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# Solutions for Chapter 1.6: THE DESIGN OF EXPERIMENTS

## Full solutions for Statistics: Informed Decisions Using Data | 4th Edition

ISBN: 9780321757272

Solutions for Chapter 1.6: THE DESIGN OF EXPERIMENTS

Solutions for Chapter 1.6
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##### ISBN: 9780321757272

Statistics: Informed Decisions Using Data was written by and is associated to the ISBN: 9780321757272. This textbook survival guide was created for the textbook: Statistics: Informed Decisions Using Data , edition: 4. Chapter 1.6: THE DESIGN OF EXPERIMENTS includes 72 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 72 problems in chapter 1.6: THE DESIGN OF EXPERIMENTS have been answered, more than 161227 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).

• 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

• Analysis of variance (ANOVA)

A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

• 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

• Bias

An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

• Central tendency

The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

• Chi-square (or chi-squared) random variable

A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

• 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.

• 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.

• Conidence level

Another term for the conidence coeficient.

• Consistent estimator

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

• Correlation

In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

• Deining relation

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

• Density function

Another name for a probability density function

• 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.

• Error variance

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

• Event

A subset of a sample space.

• 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.

• Finite population correction factor

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

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