 15.15.1: The following data are obtained from a 23 factorial experiment repl...
 15.15.2: In an experiment conducted by the Mining Engineering Department at ...
 15.15.3: In a metallurgy experiment, it is desired to test the eect of four ...
 15.15.4: A preliminary experiment is conducted to study the eects of four fa...
 15.15.5: In the study An XRay Fluorescence Method for Analyzing Polybutadie...
 15.15.6: It is important to study the eect of the concentration of the react...
 15.15.7: Consider Exercise 15.3. It is of interest to the researcher to lear...
 15.15.8: Consider Exercise 15.3 once again. Threefactor interactions are of...
 15.15.9: Consider Exercise 15.6. Use a +1 and1 scaling for high and low, res...
 15.15.10: Consider Exercise 15.5. Compute all 15 eects and do normal probabil...
 15.15.11: In Myers, Montgomery, and AndersonCook (2009), a data set is discu...
 15.15.12: Consider Exercise 15.11. Suppose there was some experimental dicult...
 15.15.13: Consider a 25 experiment where the experimental runs are on 4 diere...
 15.15.14: An experiment is described in Myers, Montgomery, and AndersonCook ...
 15.15.15: Oil producers are interested in nickel alloys that are strong and c...
 15.15.16: Suppose a second replicate of the experiment in Exercise 15.13 coul...
 15.15.17: Consider Figure 15.14, which represents a 22 factorial with 3 cente...
 15.15.18: List the aliases for the various eects in a 25 factorial experiment...
 15.15.19: (a) Obtain a 1 2 fraction of a 24 factorial design using BCD as the...
 15.15.20: Construct a 1 4 fraction of a 26 factorial design using ABCD and BD...
 15.15.21: (a) Using the dening contrasts ABCE and ABDF, obtain a 1 4 fraction...
 15.15.22: Seven factors are varied at two levels in an experiment involving o...
 15.15.23: An experiment is conducted so that an engineer can gain insight int...
 15.15.24: In an experiment conducted at the Department of Mechanical Engineer...
 15.15.25: In the study Durability of Rubber to Steel Adhesively Bonded Joints...
 15.15.26: Consider a 251 design with factors A, B, C, D, and E. Construct the...
 15.15.27: There are six factors and only eight design points can be used. Con...
 15.15.28: Consider Exercise 15.27. Construct another 263 that is dierent from...
 15.15.29: For Exercise 15.27, give all aliases for the six main eects.
 15.15.30: In Myers, Montgomery, and AndersonCook (2009), an application is d...
 15.15.31: Consider an example in which there are two control variables x1 and...
 15.15.32: Consider the following 23 factorial with control variables x1 and x...
 15.15.33: Consider Case Study 15.1 involving the injection molding data. Supp...
 15.15.34: In Case Study 15.2 involving the coal cleansing data, the percent s...
 15.15.35: Use the coal cleansing data of Exercise 15.2 on page 609 to t a mod...
 15.15.36: A2 5 factorial plan is used to build a regression model containing ...
 15.15.37: Consider the 1 16 of the 27 factorial discussed in Section 15.9. Li...
 15.15.38: Construct a PlackettBurman design for 10 variables containing 24 e...
 15.15.39: A PlackettBurman design was used to study the rheological properti...
 15.15.40: A large petroleum company in the Southwest regularly conducts exper...
 15.15.41: A2 2 factorial experiment is analyzed by the Statistics Consulting ...
 15.15.42: In the study The Use of Regression Analysis for Correcting Matrix E...
 15.15.43: Use Table 15.16 to construct a 16run design with 8 factors that is...
 15.15.44: Verify that your design in Review Exercise 15.43 is indeed resoluti...
 15.15.45: Construct a design that contains 9 design points, is orthogonal, co...
 15.15.46: Consider a design which is a 231 III with 2 center runs. Consider y...
Solutions for Chapter 15: 2k Factorial Experiments and Fractions
Full solutions for Probability and Statistics for Engineers and the Scientists  9th Edition
ISBN: 9780321629111
Solutions for Chapter 15: 2k Factorial Experiments and Fractions
Get Full SolutionsThis textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 15: 2k Factorial Experiments and Fractions includes 46 full stepbystep solutions. Since 46 problems in chapter 15: 2k Factorial Experiments and Fractions have been answered, more than 168970 students have viewed full stepbystep solutions from this chapter. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111.

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

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.

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

Bimodal distribution.
A distribution with two modes

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).

Categorical data
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

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.

Combination.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables

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.

Cook’s distance
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

Correlation
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.

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).

Density function
Another name for a probability density function

Enumerative study
A study in which a sample from a population is used to make inference to the population. See Analytic study

Error propagation
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

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

Gaussian distribution
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.