- 3.4SE: For some genetic mutations, it is thought that the frequency of the...
- 3.5SE: The Darcy-Weisbach equation states that the power- generating capac...
- 3.6SE: Let A and B represent two variants (alleles) of the DNA at a certai...
- 3.7SE: The heating capacity of a calorimeter is known to be 4 kJ/°C, with ...
- 3.9SE: The article “Insights into Present-Day Crustal Motion in the Centra...
- 3.10SE: If two gases have molar masses M1, and M2 Graham’s law states that ...
- 3.12SE: The article “Effect of Varying Solids Concentration and Organic Loa...
- 3.13SE: In the article “Measurements of the Thermal Conductivity and Therma...
- 3.14SE: A cable is made up of several parallel strands of wire. The strengt...
- 3.15SE: Refer to Exercise 14. A cable is composed of 16 wires. The strength...
- 3.16SE: The mean yield from process A is estimated to be 80 ± 5, where the ...
- 3.17SE: The flow rate of water through a cylindrical pipe is given by Q =?r...
- 3.18SE: The conversion of cyclobutane (C4 H8) to ethylene (C2 H4) is a firs...
- 3.19SE: The decomposition of nitrogen dioxide (NO2) into nitrogen monoxide ...
- 3.20SE: Two students want to measure the acceleration a of a cart rolling d...
- 3.21SE: A track has the shape of a square capped on two opposite sides by s...
- 3.22SE: If X is an unbiased measurement of a true value ?X, and U(X) is a n...
- 3.23SE: If X1,X2, ..., Xn are independent and unbiased measurements of true...
Solutions for Chapter 3: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists | 4th Edition
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
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).
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.
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.
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
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.
Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.
Coeficient of determination
See R 2 .
The probability of an event given that the random experiment produces an outcome in another event.
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
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.
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 .
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.
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).
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).
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.