 4.1SE: An airplane has 100 seats for passengers. Assume that the probabili...
 4.2SE: The number of large cracks in a length of pavement along a certain ...
 4.3SE: Pea plants contain two genes for seed color, each of which may be Y...
 4.4SE: A simple random sample X1,..., Xn is drawn from a population, and t...
 4.5SE: The Environmental Protection Agency (EPA) has contracted with your ...
 4.6SE: In the article "Occurrence and Distribution of Ammonium in Iowa Gro...
 4.7SE: Medication used to treat & certain condition is administered by syr...
 4.8SE: A certain type of plywood consists of five layers. The thicknesses ...
 4.9SE: The intake valve clearances on new engines of a certain type are no...
 4.10SE: The stiffness of a certain type of steel beam used in building cons...
 4.11SE: In a certain process, the probability of producing an defective com...
 4.12SE: A process that polishes a mirrored surface leaves an average of 2 s...
 4.13SE: Yeast cells are suspended in a liquid medium. A 2 mL sample of the ...
 4.14SE: A plate is attached to its base by 10 bolts. Each bolt is inspected...
 4.15SE: Thicknesses of shims are normally distributed with mean 1.5 mm and ...
 4.16SE: The lifetime of a microprocessor is exponentially distributed with ...
 4.17SE: The lifetime of a bearing (in years) follows the Weibull distributi...
 4.18SE: The length of time to perform an oil change at a certain shop is no...
 4.19SE: A cereal manufacturer claims that the gross weight (including packa...
 4.20SE: Someone claims that the number of hits on his website has a Poisson...
 4.21SE: A distribution sometimes used to model the largest item in a sample...
 4.22SE: An alternative to the lognormal distribution for modeling highly sk...
 4.23SE: A distribution that has been used to model tolerance levels in bioa...
 4.24SE: Radioactive mass 1 emits particles at a mean rate of ?1 per second,...
 4.25SE: Let X ~ Geom(p). Let s ? 0 be an integer.a. Show that P(X > s) = (1...
 4.26SE: A stick of length 1 is broken at a point chosen uniformly along its...
 4.27SE: Let X represent the lifetime of a component, in weeks. Let Y repres...
 4.28SE: Let X ~ Bin(n, p).a. Show that if x is an integer between 1 and n i...
 4.29SE: Let X ~ Poisson(?).a. Show that if x is a positive integer, then __...
 4.30SE: Let Z ~ N(0, 1), and let X = ?Z +µ where p and ? > 0 are constants....
Solutions for Chapter 4: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists  4th Edition
ISBN: 9780073401331
Solutions for Chapter 4
Get Full SolutionsStatistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Since 30 problems in chapter 4 have been answered, more than 263321 students have viewed full stepbystep solutions from this chapter. Chapter 4 includes 30 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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

Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chisquare with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chisquare random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chisquare random variables.

Alias
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

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

Bivariate normal distribution
The joint distribution of two normal random variables

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

Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.

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.

Correction factor
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

Correlation matrix
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the offdiagonal elements rij are the correlations between Xi and Xj .

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

Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

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

Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.

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.

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.

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

Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

False alarm
A signal from a control chart when no assignable causes are present