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# Solutions for Chapter 2: Modeling Distributions of Data

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

ISBN: 9781464108730

Solutions for Chapter 2: Modeling Distributions of Data

Solutions for Chapter 2
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##### ISBN: 9781464108730

This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2: Modeling Distributions of Data includes 24 full step-by-step solutions. This textbook survival guide was created for the textbook: The Practice of Statistics, edition: 5. The Practice of Statistics was written by and is associated to the ISBN: 9781464108730. Since 24 problems in chapter 2: Modeling Distributions of Data have been answered, more than 8849 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
• 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

• 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.

• Categorical data

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

• Comparative experiment

An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

• Conidence coeficient

The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.

• Control limits

See Control chart.

• Cook’s distance

In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

• 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).

• 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.

• Degrees of freedom.

The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

• Density function

Another name for a probability density function

• Discrete distribution

A probability distribution for a discrete random variable

• Dispersion

The amount of variability exhibited by data

• 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 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.

• Expected value

The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

• Gamma random variable

A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

• Harmonic mean

The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .

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