- 3.1: Assume that X, Y , and Z are independent measurements with X = 25 1...
- 3.2: Assume that X, Y , and Z are independent measurements, and that the...
- 3.3: An item is to be constructed by laying three components in a row. T...
- 3.4: For some genetic mutations, it is thought that the frequency of the...
- 3.5: The DarcyWeisbach equation states that the powergenerating capacity...
- 3.6: Let A and B represent two variants (alleles) of the DNA at a certai...
- 3.7: The heating capacity of a calorimeter is known to be 4 kJ/C, with n...
- 3.8: Sixteen independent measurements were made of the resistance of a r...
- 3.9: The article Insights into Present-Day Crustal Motion in the Central...
- 3.10: If two gases have molar masses M1 and M2, Grahams law states that t...
- 3.11: A piece of plywood is composed of five layers. The two outer layers...
- 3.12: The article Effect of Varying Solids Concentration and Organic Load...
- 3.13: In the article Measurements of the Thermal Conductivity and Thermal...
- 3.14: A cable is made up of several parallel strands of wire. The strengt...
- 3.15: Refer to Exercise 14. A cable is composed of 16 wires. The strength...
- 3.16: The mean yield from process A is estimated to be 80 5, where the un...
- 3.17: The flow rate of water through a cylindrical pipe is given by Q = r...
- 3.18: The conversion of cyclobutane (C4H8) to ethylene (C2H4) is a first-...
- 3.19: The decomposition of nitrogen dioxide (NO2) into nitrogen monoxide ...
- 3.20: Two students want to measure the acceleration a of a cart rolling d...
- 3.21: A track has the shape of a square capped on two opposite sides by s...
- 3.22: If X is an unbiased measurement of a true value X , and U(X) is a n...
- 3.23: If X is an unbiased measurement of a true value X , and U(X) is a n...
Solutions for Chapter 3: Propagation of Error
Full solutions for Statistics for Engineers and Scientists | 4th Edition
a-error (or a-risk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).
Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
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
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.
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
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
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.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
A probability distribution for a continuous random variable.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
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
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
The response variable in regression or a designed experiment.
A matrix that provides the tests that are to be conducted in an experiment.
A probability distribution for a discrete random variable
A series of tests in which changes are made to the system under study
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
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 .