×
×

# Solutions for Chapter 4.12: Applied Statistics and Probability for Engineers 6th Edition

## Full solutions for Applied Statistics and Probability for Engineers | 6th Edition

ISBN: 9781118539712

Solutions for Chapter 4.12

Solutions for Chapter 4.12
4 5 0 413 Reviews
21
1
##### ISBN: 9781118539712

Since 51 problems in chapter 4.12 have been answered, more than 174326 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712. Chapter 4.12 includes 51 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions.

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).

A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

• 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

• Biased estimator

Unbiased estimator.

• Binomial random variable

A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

• Causal variable

When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

• Central limit theorem

The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

• Conditional probability density function

The probability density function of the conditional probability distribution of a continuous random variable.

• Convolution

A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

• 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.

• Cumulative distribution function

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

• Dependent variable

The response variable in regression or a designed experiment.

• Error propagation

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

• Estimator (or point estimator)

A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.

• 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.

• Fixed factor (or fixed effect).

In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

• Fraction defective control chart

See P chart

• 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.

• Geometric random variable

A discrete random variable that is the number of Bernoulli trials until a success occurs.

×