Advanced Engineering Mathematics 5th Edition - Solutions by Chapter

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 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

The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

A set of rules that probabilities deined on a sample space must follow. See Probability

Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

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

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

The variance of the conditional probability distribution of a random variable.

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.

Formulas used to determine the number of elements in sample spaces and events.

Another name for factors that are arranged in a factorial experiment.

A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

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

W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

The numerical value of a point estimator.

A subset of a sample space.

A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

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.

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.