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# Solutions for Chapter 13-2: THE COMPLETELY RANDOMIZED SINGLE-FACTOR EXPERIMENT

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

ISBN: 9780471204541

Solutions for Chapter 13-2: THE COMPLETELY RANDOMIZED SINGLE-FACTOR EXPERIMENT

Solutions for Chapter 13-2
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##### ISBN: 9780471204541

Since 20 problems in chapter 13-2: THE COMPLETELY RANDOMIZED SINGLE-FACTOR EXPERIMENT have been answered, more than 22675 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9780471204541. Chapter 13-2: THE COMPLETELY RANDOMIZED SINGLE-FACTOR EXPERIMENT includes 20 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.

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.

• 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

• Arithmetic mean

The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

• Average

See Arithmetic mean.

• 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.

• Conditional probability

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

• 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.

• Critical region

In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

• 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.

• Crossed factors

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

• Curvilinear regression

An expression sometimes used for nonlinear regression models or polynomial regression models.

• 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.

• Distribution free method(s)

Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

• Error mean square

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

• F distribution.

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.

• Fractional factorial experiment

A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

• 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 .

• Goodness of fit

In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.

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