Solutions for Chapter 15: Sums and Products
Full solutions for Mathematical Statistics with Applications  8th Edition
ISBN: 9780321807090
Solutions for Chapter 15: Sums and Products
Get Full SolutionsThis textbook survival guide was created for the textbook: Mathematical Statistics with Applications, edition: 8. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780321807090. Chapter 15: Sums and Products includes 1 full stepbystep solutions. Since 1 problems in chapter 15: Sums and Products have been answered, more than 280 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Adjusted R 2
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.

Attribute
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.

Average run length, or ARL
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.

Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

Central tendency
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

Chance cause
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.

Conditional probability
The probability of an event given that the random experiment produces an outcome in another event.

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

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

Control limits
See Control chart.

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).

Covariance
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

Critical value(s)
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.

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

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

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

Discrete random variable
A random variable with a inite (or countably ininite) range.

Exponential random variable
A series of tests in which changes are made to the system under study

Geometric mean.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .