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Solutions for Chapter 10.7: Comparing Two Population Variances
Full solutions for Introduction to Probability and Statistics 1  14th Edition
ISBN: 9781133103752
Solutions for Chapter 10.7: Comparing Two Population Variances
Get Full SolutionsIntroduction to Probability and Statistics 1 was written by and is associated to the ISBN: 9781133103752. Since 61 problems in chapter 10.7: Comparing Two Population Variances have been answered, more than 9730 students have viewed full stepbystep solutions from this chapter. Chapter 10.7: Comparing Two Population Variances includes 61 full stepbystep solutions. This textbook survival guide was created for the textbook: Introduction to Probability and Statistics 1, edition: 14. This expansive textbook survival guide covers the following chapters and their solutions.

aerror (or arisk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

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.

All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

Alternative hypothesis
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

Backward elimination
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

Confounding
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

Conidence level
Another term for the conidence coeficient.

Consistent estimator
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

Control chart
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the incontrol value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be incontrol, or free from assignable causes. Points beyond the control limits indicate an outofcontrol process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

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.

Covariance matrix
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 offdiagonal elements are the covariances between Xi and Xj . Also called the variancecovariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

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

Decision interval
A parameter in a tabular CUSUM algorithm that is determined from a tradeoff between false alarms and the detection of assignable causes.

Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.

Empirical model
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

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.

Expected value
The expected value of a random variable X is its longterm 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.

Experiment
A series of tests in which changes are made to the system under study

Fraction defective control chart
See P chart

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