- 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 droppe...
- 7.3SE: Eruptions of the Old Faithful geyser in Yellowstone National Park t...
- 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 m...
- 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 whi...
- 7.13SE: Monitoring the yield of a particular chemical reaction at various r...
- 7.14SE: The article “Approach to Confidence Interval Estimation for Curve N...
- 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 Proper...
- 7.18SE: The article “Polyhedral Distortions in Tourmaline” (A. Ertl, J. Hug...
- 7.19SE: Consider the model y = ?x+?, where the intercept of the line is kno...
- 7.20SE: Use Equation (7.34) (page 541) to show that
- 7.21SE: Use Equation (7.35) (page 541) to show that
- 7.22SE: Use Equation (7.34) (page 541) 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
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.
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
Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
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.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A probability distribution for a continuous random variable.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
See Control chart.
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 .
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
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
The response variable in regression or a designed experiment.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
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
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
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