- 7.1SE: ?The Beer–Lambert law relates the absorbance A of a solution to the...
- 7.2SE: ?In a test of military ordnance, a large number of bombs were dropp...
- 7.3SE: ?Eruptions of the Old Faithful geyser in Yellowstone National Park ...
- 7.4SE: Refer to Exercise 3.a. Plot the residuals versus the fitted values....
- 7.5SE: ?A chemist is calibrating a spectrophotometer that will be used to ...
- 7.6SE: The article “Experimental Measurement of Radiative Heat Transfer in...
- 7.7SE: The article “A Robust Optimization Approach for the Capacitated Veh...
- 7.8SE: The article “Optimization of Medium Composition for Lipase Producti...
- 7.9SE: The article “Copper Oxide Mounted on Activated Carbon as Catalyst f...
- 7.10SE: The article “The Role of Niche Breadth, Resource Availability and R...
- 7.11SE: The article “Estimating Population Abundance in Plant Species with ...
- 7.12SE: ?A materials scientist is experimenting with a new material with wh...
- 7.13SE: Monitoring the yield of a particular chemical reaction at various r...
- 7.14SE: ?The article “Approach to Confidence Interval Estimation for Curve ...
- 7.15SE: Refer to Exercise 14. Someone wants to compute a 95% confidence int...
- 7.16SE: During the production of boiler plate, test pieces are subjected to...
- 7.17SE: ?The article “Low-Temperature Heat Capacity and Thermodynamic Prope...
- 7.18SE: ?The article “Polyhedral Distortions in Tourmaline” (A. Ertl, J. Hu...
- 7.19SE: ?Consider the model y = ?x +?, where the intercept of the line is k...
- 7.20SE: ?Use Equation (7.34) (page 545) to show that
- 7.21SE: ?Use Equation (7.35) (page 545) to show that
- 7.22SE: ?Use Equation (7.34) (page 545) to derive the formula
Solutions for Chapter 7: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists | 4th Edition
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
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
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
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
The joint probability distribution of two random variables.
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.
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.
Coeficient of determination
See R 2 .
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
A probability distribution for a continuous random variable.
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.
Defects-per-unit control chart
See U chart
Error of estimation
The difference between an estimated value and the true value.
Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
A property of a collection of events that indicates that their union equals the sample space.
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.
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
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.
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 .