Advanced Engineering Mathematics 5th Edition - Solutions by Chapter

In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

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.

See Arithmetic mean.

A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

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.

A random variable with an interval (either inite or ininite) of real numbers for its range.

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.

The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.

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

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

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.

Another name for a cumulative distribution function.

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.

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

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

In statistical quality control, that portion of a number of units or the output of a process that is defective.

Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.

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 .