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# Solutions for Chapter 9-4: HYPOTHESIS TESTS ON THE VARIANCE AND STANDARD DEVIATION OF A NORMAL POPULATION

## Full solutions for Applied Statistics and Probability for Engineers | 3rd Edition

ISBN: 9780471204541

Solutions for Chapter 9-4: HYPOTHESIS TESTS ON THE VARIANCE AND STANDARD DEVIATION OF A NORMAL POPULATION

Solutions for Chapter 9-4
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##### ISBN: 9780471204541

This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 3. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9780471204541. This expansive textbook survival guide covers the following chapters and their solutions. Since 7 problems in chapter 9-4: HYPOTHESIS TESTS ON THE VARIANCE AND STANDARD DEVIATION OF A NORMAL POPULATION have been answered, more than 19336 students have viewed full step-by-step solutions from this chapter. Chapter 9-4: HYPOTHESIS TESTS ON THE VARIANCE AND STANDARD DEVIATION OF A NORMAL POPULATION includes 7 full step-by-step solutions.

Key Statistics Terms and definitions covered in this textbook
• 2 k factorial experiment.

A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

• 2 k p - factorial experiment

A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

• 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

• Bernoulli trials

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

• Bias

An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

• Biased estimator

Unbiased estimator.

• Bivariate normal distribution

The joint distribution of two normal random variables

• Central composite design (CCD)

A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.

• Chi-square test

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

• Conidence level

Another term for the conidence coeficient.

• Control chart

A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control 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 in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control 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.

• 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).

• Decision interval

A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

• Deming’s 14 points.

A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

• Density function

Another name for a probability density function

• Eficiency

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.

• Error mean square

The error sum of squares divided by its number of degrees of freedom.

• Exhaustive

A property of a collection of events that indicates that their union equals the sample space.

• Exponential random variable

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

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