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# Solutions for Chapter 1.3: Describing Quantitative Data with Numbers

## Full solutions for The Practice of Statistics | 5th Edition

ISBN: 9781464108730

Solutions for Chapter 1.3: Describing Quantitative Data with Numbers

Solutions for Chapter 1.3
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##### ISBN: 9781464108730

The Practice of Statistics was written by and is associated to the ISBN: 9781464108730. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 1.3: Describing Quantitative Data with Numbers includes 35 full step-by-step solutions. This textbook survival guide was created for the textbook: The Practice of Statistics, edition: 5. Since 35 problems in chapter 1.3: Describing Quantitative Data with Numbers have been answered, more than 3576 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

• a-error (or a-risk)

In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• 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.

• 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 interval

If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

• 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.

• Correlation coeficient

A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

• 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.

• Cumulative normal distribution function

The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

• Defect

Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

• Dependent variable

The response variable in regression or a designed experiment.

• Error variance

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

• Finite population correction factor

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

• Forward selection

A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

• Fractional factorial experiment

A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

• Frequency distribution

An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

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