 6.2.30E: An article in Technometrics (1977, Vol. 19, p. 425) presented the f...
 6.2.25E: For the data in Exercise 620,(a) Construct a stemandleaf diagram...
 6.2.26E: For the data in Exercise 621,(a) Construct a stemandleaf diagram...
 6.2.27E: A backtoback stemandleaf display on two data sets is conducted ...
 6.2.28E: When will the median of a sample be equal to the sample mean?
 6.2.29E: When will the median of a sample be equal to the mode?
 6.2.31E: The following data are the numbers of cycles to failure of aluminum...
 6.2.32E: The percentage of cotton in material used to manufacture men’s shir...
 6.2.33E: The following data represent the yield on 90 consecutive batches of...
 6.2.34E: Calculate the sample median, mode, and mean of the data in Exercise...
 6.2.35E: Calculate the sample median, mode, and mean of the data in Exercise...
 6.2.36E: Calculate the sample median, mode, and mean for the data in Exercis...
 6.2.37E: The net energy consumption (in billions of kilowatthours) for count...
 6.2.38E: The female students in an undergraduate engineering core course at ...
 6.2.39E: The shear strengths of 100 spot welds in a titanium alloy follow. C...
 6.2.40E: An important quality characteristic of water is the concentration o...
 6.2.41E: The United States Golf Association tests golf balls to ensure that ...
 6.2.42E: A semiconductor manufacturer produces devices used as central proce...
 6.2.43E: A group of wine enthusiasts tastetested a pinot noir wine from Ore...
 6.2.44E: In their book Introduction to Linear Regression Analysis (5th editi...
 6.2.45E: In Exercise 638, we presented height data that were selfreported ...
Solutions for Chapter 6.2: Applied Statistics and Probability for Engineers 6th Edition
Full solutions for Applied Statistics and Probability for Engineers  6th Edition
ISBN: 9781118539712
Solutions for Chapter 6.2
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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.

Analytic study
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

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

Bayes’ theorem
An equation for a conditional probability such as PA B (  ) in terms of the reverse conditional probability PB A (  ).

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

Biased estimator
Unbiased estimator.

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.

Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

Conditional variance.
The variance of the conditional probability distribution of a random variable.

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 interval
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

Contingency table.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

Contour plot
A twodimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

Contrast
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

Degrees of freedom.
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.

Event
A subset of a sample space.

F distribution.
The distribution of the random variable deined as the ratio of two independent chisquare random variables, each divided by its number of degrees of freedom.

Firstorder model
A model that contains only irstorder terms. For example, the irstorder response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irstorder model is also called a main effects model

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.

Hat matrix.
In multiple regression, the matrix H XXX X = ( ) ? ? 1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .